Ultimo aggiornamento:  2023/03/13

*** Integrali di Fermi-Dirac

@ARTICLE{Mc-St,
AUTHOR="J. C. McDougall and E. C. Stoner",
TITLE="The computation of {F}ermi-{D}irac functions",
JOURNAL=PTRSA,
VOLUME=237,
PAGES={67--104},
YEAR=1938}

@ARTICLE{Rhodes,
AUTHOR="P. Rhodes",
TITLE="{F}ermi-{D}irac function of integral order",
JOURNAL=PRSLA,
VOLUME=204,
PAGES={396--405},
YEAR=1950}

@ARTICLE{Jo-Sh,
AUTHOR="V. A. Johnson and F. M. Shipley",
TITLE="The Adiabatic {H}all Effect in Semiconductors",
JOURNAL=PR,
VOLUME=90,
NUMBER=4,
PAGES={523--529},
YEAR=1953}

@ARTICLE{1955Beer_HPA,
AUTHOR="A. C. Beer and M. N. Chase and P. F. Choquard",
TITLE="Extension of {M}c{D}ougall-{S}toner tables of the {F}ermi-{D}irac functions",
JOURNAL=HPA,
VOLUME=28,
PAGES={529--542},
YEAR=1955}

@ARTICLE{Dingle-1,
AUTHOR="R. B. Dingle",
TITLE="The {F}ermi-{D}irac Integrals {${\cal F}_{p}(\eta)=(p!)^{-1} \int_{0}^{\infty}\epsilon^{p}(\mathrm{e}^{\epsilon-\eta}+1)^{-1} \mathrm{d}\epsilon$}",
JOURNAL=ASRB,
VOLUME=6,
PAGES={225--239},
YEAR=1957}

@ARTICLE{Dingle-5,
AUTHOR="R. B. Dingle",
TITLE="Asymptotic expansions and converging factors {III}.  {G}amma, psi and polygamma functions, and {F}ermi-{D}irac and {B}ose-{E}instein integrals",
JOURNAL=PRSLA,
VOLUME=244,
PAGES={484--490},
YEAR=1958}

@ARTICLE{We-Ra,
AUTHOR="H. Werner and G. Raymann",
TITLE="An Approximation to the {F}ermi Integral {$F_{1/2}(x)$}",
JOURNAL=MC,
VOLUME=17,
NUMBER=82,
PAGES={193--194},
MONTH=APR,
YEAR=1963}

@ARTICLE{Battocletti,
AUTHOR="F. E. Battocletti",
TITLE="Polynomial Approximation of the {F}ermi Integral",
JOURNAL=PIEEE,
VOLUME=53,
PAGES={2162--2163},
MONTH=DEC,
YEAR=1965}

@ARTICLE{Jones,
AUTHOR="E. L. Jones",
TITLE="Rational {C}hebyshev Approximation of the {F}ermi-{D}irac Integrals",
JOURNAL=PIEEE,
VOLUME=54,
NUMBER=4,
PAGES={708--709},
MONTH=APR,
YEAR=1966}

@ARTICLE{Co-Th,
AUTHOR="W. J. Cody and Thacher, Jr., H. C.",
TITLE="Rational {C}hebyshev Approximations for {F}ermi-{D}irac Integrals of Orders $-\frac{1}{2}$, $\frac{1}{2}$ and $\frac{3}{2}$",
JOURNAL=MC,
VOLUME=21,
NUMBER=97,
PAGES={30--40},
YEAR=1967}

@ARTICLE{Jo-Di-2,
AUTHOR="W. B. Joyce and R. W. Dixon",
TITLE="Analytic approximations for the {F}ermi energy of an ideal {F}ermi gas",
JOURNAL=APL,
VOLUME=31,
NUMBER=5,
PAGES={354--356},
MONTH=SEP,
YEAR=1977}

@ARTICLE{1978Bednarczyk_PLA,
DOI={10.1016/0375-9601(78)90283-9},
AUTHOR="D. Bednarczyk and J. Bednarczyk",
TITLE="The approximation of the {F}ermi-{D}irac integral {${\cal F}_{1/2}(\eta)$}",
JOURNAL=PLA,
VOLUME=64,
NUMBER=4,
PAGES={409--410},
MONTH=JAN,
YEAR=1978}

@ARTICLE{Joyce-1,
AUTHOR="W. B. Joyce",
TITLE="Analytic approximations for the {F}ermi energy in {(Al,Ga)As}",
JOURNAL=APL,
VOLUME=32,
NUMBER=10,
PAGES={680--681},
MONTH=MAY,
YEAR=1978}

@ARTICLE{NGNilsson,
AUTHOR="N. G. Nilsson",
TITLE="Empirical approximations for the {F}ermi energy in a semiconductor with parabolic bands",
JOURNAL=APL,
VOLUME=33,
NUMBER=7,
PAGES={653--654},
MONTH=OCT,
YEAR=1978}

@ARTICLE{Ay-Se-Mi-1,
AUTHOR="X. Aymerich-Humet and F. Serra-Mestres and J. Mill{\'a}n",
TITLE="An Analytical Approximation for the {F}ermi-{D}irac integral {${\cal F}_{3/2}(\eta)$}",
JOURNAL=SSE,
VOLUME=24,
NUMBER=10,
PAGES={981--982},
YEAR=1981}

@ARTICLE{Ba-De-Ma,
AUTHOR="A. Ba{\~n}uelos and R. A. Depine and R. C. Mancini",
TITLE="A Program for Computing the {F}ermi-{D}irac Functions",
JOURNAL=CPC,
VOLUME=21,
PAGES={315--322},
YEAR=1981}

@ARTICLE{Selvakumar,
AUTHOR="C. R. Selvakumar",
TITLE="Approximation to {F}ermi-{D}irac Integrals and Their Use in Device Analysis",
JOURNAL=PIEEE,
VOLUME=70,
NUMBER=5,
PAGES={516--518},
MONTH=MAY,
YEAR=1982}

@ARTICLE{1982Blakemore_SSE,
AUTHOR="J. S. Blakemore",
TITLE="Approximation for {F}ermi-{D}irac Integrals, Especially the Function {${\cal F}_{1/2}(\eta)$} Used to Describe Electron Density in a Semiconductor",
JOURNAL=SSE,
VOLUME=25,
NUMBER=11,
PAGES={1067--1076},
YEAR=1982}

@ARTICLE{Ay-Se-Mi-2,
AUTHOR="X. Aymerich-Humet and F. Serra-Mestres and J. Mill{\'a}n",
TITLE="A generalized approximation of the {F}ermi-{D}irac integrals",
JOURNAL=JAP,
VOLUME=54,
NUMBER=5,
PAGES={2850--2851},
MONTH=MAY,
YEAR=1983}

@ARTICLE{Ab-Mo,
AUTHOR="S. T. Abidi and S. N. Mohammad",
TITLE="Approximation for the {F}ermi-{D}irac integral with applications to degenerately doped solar cells and other semiconductor devices",
JOURNAL=JAP,
VOLUME=56,
NUMBER=11,
PAGES={3341--3343},
MONTH=DEC,
YEAR=1984}

@ARTICLE{Ga-Mi,
AUTHOR="W. Gautschi and G. V. Milovanovi{\v{c}}",
TITLE="{G}aussian Quadrature Involving {E}instein and {F}ermi Functions With an Application to Summation of Series",
JOURNAL=MC,
VOLUME=44,
NUMBER=169,
PAGES={177--190},
MONTH=JAN,
YEAR=1985}

@ARTICLE{Va-Pu-1,
AUTHOR="Van Halen, P. and D. L. Pulfrey",
TITLE="Accurate, short series approximations to {F}ermi-{D}irac integrals of order -1/2, 1/2, 1, 3/2, 2, 5/2, 3, and 7/2",
JOURNAL=JAP,
VOLUME=57,
NUMBER=12,
PAGES={5271--5274},
MONTH=JUN,
YEAR=1985}

@ARTICLE{We-Hi,
AUTHOR="M. H. Wendel and E. R. Hilf",
TITLE="Generalized moments applied to {F}ermi-type functions",
JOURNAL=JMP,
VOLUME=26,
NUMBER=7,
PAGES={1570--1575},
MONTH=JUL,
YEAR=1985}

@ARTICLE{Va-Pu-2,
AUTHOR="Van Halen, P. and D. L. Pulfrey",
TITLE="Erratum: ``{A}ccurate, short series approximations to {F}ermi-{D}irac integrals of order -1/2, 1/2, 1, 3/2, 2, 5/2, 3, and 7/2'' [{J}. {A}ppl. {P}hys. 57, 5271 (1985)]",
JOURNAL=JAP,
VOLUME=59,
NUMBER=6,
PAGES={2264--2265},
MONTH=MAR,
YEAR=1986}

@ARTICLE{Fu-Ri,
AUTHOR="L. W. Fullerton and G. A. Rinker",
TITLE="Generalized {F}ermi-{D}irac Integrals -- {FD}, {FDG}, {FDH}",
JOURNAL=CPC,
VOLUME=39,
PAGES={181--185},
YEAR=1986}

@ARTICLE{Ag-Es-Ko,
AUTHOR="V. C. Aguilera-Navarro and G. A. Est{\'e}vez and A. Kostecki",
TITLE="A note on the {F}ermi-{D}irac integral function",
JOURNAL=JAP,
VOLUME=63,
NUMBER=8,
PAGES={2848--2850},
MONTH=APR,
YEAR=1988}

@ARTICLE{Oh-Ko-Ni,
AUTHOR="I. J. Ohsugi and T. Kojima and I. Nishida",
TITLE="A calculational procedure of the {F}ermi-{D}irac integral with an arbitrary real index by means of a numerical integration technique",
JOURNAL=JAP,
VOLUME=63,
NUMBER=10,
PAGES={5179--5181},
MONTH=MAY,
YEAR=1988}

@ARTICLE{Unger,
AUTHOR="K. Unger",
TITLE="Reversible Formulae to Approximate {F}ermi integrals",
JOURNAL=PSSB,
VOLUME=149,
PAGES={K141--K144},
YEAR=1988}

@ARTICLE{Ch-Iz,
AUTHOR="T. Y. Chang and A. Izabelle",
TITLE="Full range analytic approximations for {F}ermi energy and {F}ermi-{D}irac integral {${\cal F}_{-1/2}(\eta)$} in terms of {${\cal F}_{1/2}(\eta)$}",
JOURNAL=JAP,
VOLUME=65,
NUMBER=5,
PAGES={2162--2164},
MONTH=MAR,
YEAR=1989}

@ARTICLE{Cloutman,
AUTHOR="L. D. Cloutman",
TITLE="Numerical evaluation of the {F}ermi-{D}irac integrals",
JOURNAL=APJSS,
VOLUME=71,
PAGES={677--699},
MONTH=NOV,
YEAR=1989}

@ARTICLE{Pichon,
AUTHOR="B. Pichon",
TITLE="Numerical calculation of the generalized {F}ermi-{D}irac
integrals",
JOURNAL=CPC,
VOLUME=55,
PAGES={127--136},
YEAR=1989}

@ARTICLE{Sagar,
AUTHOR="R. P. Sagar",
TITLE="On the evaluation of the {F}ermi-{D}irac integrals",
JOURNAL=APJ,
VOLUME=376,
PAGES={364--366},
MONTH=JUL,
YEAR=1991}

@ARTICLE{VanCong,
AUTHOR="Van Cong, H.",
TITLE="New Series Representation of {F}ermi-{D}irac Integral {$F_{j}(-\infty < a \ll \infty)$} for Arbitrary $j > -1$, and its Effect on {$F_{j}(a \geq 0_{+})$} for Integer $j \geq 0$",
JOURNAL=SSE,
VOLUME=34,
NUMBER=5,
PAGES={489--492},
YEAR=1991}

@ARTICLE{Va-Do,
AUTHOR="Van Cong, H. and B. Doan-Khanh",
TITLE="Simple Accurate General Expression of the {F}ermi-{D}irac Integral {$F_{j}(a)$} for Arbitrary $a$ and $j > -1$",
JOURNAL=SSE,
VOLUME=35,
NUMBER=7,
PAGES={949--951},
YEAR=1992}

@ARTICLE{Va-De,
AUTHOR="Van Cong, H. and G. Debiais",
TITLE="A simple accurate expression of the reduced {F}ermi energy for any reduced carrier density",
JOURNAL=JAP,
VOLUME=73,
NUMBER=3,
PAGES={1545--1546},
MONTH=FEB,
YEAR=1993}

@ARTICLE{Sm-Ro,
AUTHOR="A. W. Smith and A. Rohatgi",
TITLE="Re-evaluation of the derivatives of the half order {F}ermi integrals",
JOURNAL=JAP,
VOLUME=73,
NUMBER=11,
PAGES={7030--7034},
MONTH=JUN,
YEAR=1993}

@ARTICLE{1993Goano_SSE,
DOI={10.1016/0038-1101(93)90143-E},
AUTHOR="M. Goano",
TITLE="Series Expansion of the {F}ermi-{D}irac Integral {${\cal F}_{j}(x)$} over the Entire Domain of Real $j$ and $x$",
JOURNAL=SSE,
VOLUME=36,
NUMBER=2,
PAGES={217--221},
YEAR=1993}

@ARTICLE{93Natarajan_CPC,
AUTHOR="A. Natarajan and N. Mohankumar",
TITLE="On the numerical evaluation of the generalised {F}ermi-{D}irac integrals",
JOURNAL=CPC,
VOLUME=76,
PAGES={48--50},
YEAR=1993}

@ARTICLE{Wo-Mc-Li,
AUTHOR="S. A. Wong and S. P. McAlister and Z.-H. Li",
TITLE="A Comparison of Some Approximations for the {F}ermi-{D}irac Integral of order 1/2",
JOURNAL=SSE,
VOLUME=37,
NUMBER=1,
PAGES={61--64},
YEAR=1994}

@ARTICLE{Abuelmaatti_SSE,
AUTHOR="M. T. Abuelma'atti",
TITLE="Approximations for the {F}ermi-{D}irac Integrals {$F_{j}(x)$}",
JOURNAL=SSE,
VOLUME=37,
NUMBER=7,
PAGES={1367--1369},
YEAR=1994}

@ARTICLE{1995Goano_ACMMS,
DOI={10.1145/210089.210090},
AUTHOR="M. Goano",
TITLE="Algorithm 745. {C}omputation of the complete and incomplete {F}ermi-{D}irac integral",
JOURNAL=ACMMS,
VOLUME=21,
NUMBER=3,
PAGES={221--232},
MONTH=SEP,
YEAR=1995}

@ARTICLE{95Mohankumar_PSSB,
AUTHOR="N. Mohankumar and A. Natarajan",
TITLE="The Accurate Numerical Evaluation of Half-Order {F}ermi-{D}irac Integrals",
JOURNAL=PSSB,
VOLUME=188,
PAGES={635--644},
YEAR=1995}

@ARTICLE{96Mohankumar_APJ,
AUTHOR="N. Mohankumar and A. Natarajan",
TITLE="A note on the evaluation of the generalized {F}ermi-{D}irac integral",
JOURNAL=APJ,
VOLUME=458,
PAGES={233--235},
MONTH=FEB,
YEAR=1996}

@ARTICLE{1997Goano_ACMMS,
AUTHOR="M. Goano",
TITLE="Remark on {A}lgorithm 745",
JOURNAL=ACMMS,
VOLUME=23,
NUMBER=2,
PAGES=295,
MONTH=JUN,
YEAR=1997}

@ARTICLE{97Mohankumar_CPC,
AUTHOR="N. Mohankumar and A. Natarajan",
TITLE="The accurate evaluation of a particular {F}ermi-{D}irac integral",
JOURNAL=CPC,
VOLUME=101,
PAGES={47--53},
YEAR=1997}

@ARTICLE{MacLeod,
AUTHOR="A. J. MacLeod",
TITLE="Algorithm 779: {F}ermi-{D}irac Functions of Order -1/2, 1/2, 3/2, 5/2",
JOURNAL=ACMMS,
VOLUME=24,
NUMBER=1,
PAGES={1--12},
MONTH=MAR,
YEAR=1998}


*** Integrali di Fermi-Dirac:  applicazioni

@ARTICLE{1982Blakemore_JAP,
AUTHOR="J. S. Blakemore",
TITLE="Intrinsic Density {$n_{i}(T)$} in {GaAs}: {D}educed from Band Gap and Effective Mass Parameters and Derived Indipendently from {Cr} Acceptor Capture and Emission Coefficients",
JOURNAL=JAP,
VOLUME=53,
NUMBER=1,
PAGES={520--531},
MONTH=JAN,
YEAR=1982}

@ARTICLE{Joyce-4,
AUTHOR="W. B. Joyce",
TITLE="Expression for the {F}ermi Energy in Narrow-Bandgap Semiconductors",
JOURNAL=JQE,
VOLUME={QE-19},
NUMBER=11,
PAGES={1625--1627},
MONTH=NOV,
YEAR=1983}

@ARTICLE{Al-Fi,
AUTHOR="V. Altschul and E. Finkman",
TITLE="Simple approximation for {F}ermi energy in nonparabolic semiconductors",
JOURNAL=APL,
VOLUME=58,
NUMBER=9,
PAGES={942--944},
MONTH=MAR,
YEAR=1991}

@ARTICLE{Gh-Bu,
AUTHOR="K. P. Ghatak and S. N. Biswas",
TITLE="On the diffusivity-mobility ratio in small-gap semiconductors in the presence of a strong magnetic field:  {T}heory and suggestion for experimental determination",
JOURNAL=JAP,
VOLUME=70,
NUMBER=8,
PAGES={4309--4316},
MONTH=OCT,
YEAR=1991}

@ARTICLE{Beresford-1,
AUTHOR="R. Beresford",
TITLE="Analytical approximations for the {F}ermi energy of an ideal {F}ermi gas obeying a nonparabolic dispersion relation",
JOURNAL=JAP,
VOLUME=70,
NUMBER=9,
PAGES={5156--5158},
MONTH=NOV,
YEAR=1991}

@ARTICLE{Beresford-2,
AUTHOR="R. Beresford",
TITLE="Statistical properties of an ideal nonparabolic {F}ermi gas",
JOURNAL=JAP,
VOLUME=70,
NUMBER=11,
PAGES={6834--6841},
MONTH=DEC,
YEAR=1991}


*** Trasformazioni conformi

@ARTICLE{Lewin,
AUTHOR="L. Lewin",
TITLE="Note on the Inversion of the {S}chwarz-{C}hristoffel Conformal Transformation",
JOURNAL=TMTT,
VOLUME={MTT-19},
NUMBER=6,
PAGES={35--40},
MONTH=JUN,
YEAR=1971}

@ARTICLE{Trefethen,
AUTHOR="L. N. Trefethen",
TITLE="Numerical Computation of the {S}chwarz-{C}hristoffel Transformation",
JOURNAL=SIAMC,
VOLUME=1,
NUMBER=1,
PAGES={82--102},
MONTH=MAR,
YEAR=1980}

@ARTICLE{Costamagna-1,
AUTHOR="E. Costamagna",
TITLE="On the Numerical Inversion of the {S}chwarz-{C}hristoffel Conformal Transformation",
JOURNAL=TMTT,
VOLUME={MTT-35},
NUMBER=1,
PAGES={35--40},
MONTH=JAN,
YEAR=1987}

@ARTICLE{Ho-Tr,
AUTHOR="L. H. Howell and L. N. Trefethen",
TITLE="A Modified {S}chwarz-{C}hristoffel Transformation for Elongated Regions",
JOURNAL=SIAMC,
VOLUME=11,
NUMBER=5,
PAGES={928--949},
MONTH=SEP,
YEAR=1990}

@ARTICLE{Ch-Sc,
AUTHOR="M. A. Chaudhry and R. Schinzinger",
TITLE="Numerical Computation of the {S}chwarz-{C}hristoffel Transformation Parameters for Conformal Mapping of Arbitrarily Shaped Polygons with Finite Vertices",
JOURNAL=COMPE,
VOLUME=11,
NUMBER=1,
PAGES={263--275},
YEAR=1992}

@ARTICLE{Chaudhry,
AUTHOR="M. A. Chaudhry",
TITLE="An Extended {S}chwarz-{C}hristoffel Transformation for Numerical Mapping of Polygons with Curved Segments",
JOURNAL=COMPE,
VOLUME=11,
NUMBER=2,
PAGES={277--293},
YEAR=1992}

@ARTICLE{1996Driscoll_ACMMS,
AUTHOR="T. A. Driscoll",
TITLE="Algorithm 756: {A} {MATLAB} Toolbox for {S}chwarz-{C}hristoffel Mapping",
JOURNAL=ACMMS,
VOLUME=22,
NUMBER=2,
PAGES={168--186},
MONTH=JUN,
YEAR=1996}

@ARTICLE{Costamagna-2,
AUTHOR="E. Costamagna",
TITLE="Integration formulas for numerical calculation of the {S}chwarz-{C}hristoffel conformal transformation",
JOURNAL=MOTL,
VOLUME=15,
NUMBER=4,
PAGES={219--224},
MONTH=JUL,
YEAR=1997}

@ARTICLE{Hu,
AUTHOR="C. Hu",
TITLE="Algorithm 785: {A} Software Package for Computing {S}chwarz-{C}hristoffel Conformal Transformation for Doubly Connected Polygonal Regions",
JOURNAL=ACMMS,
VOLUME=24,
NUMBER=3,
PAGES={317--333},
MONTH=SEP,
YEAR=1998}

@ARTICLE{Dr-Va,
AUTHOR="T. A. Driscoll and S. A. Vavasis",
TITLE="Numerical Conformal Mapping Using Cross-Ratios and {D}elaunay Triangulation",
JOURNAL=SIAMS,
VOLUME=19,
NUMBER=6,
PAGES={1783--1803},
MONTH=NOV,
YEAR=1998}

@ARTICLE{Costamagna-3,
AUTHOR="E. Costamagna",
TITLE="Error-masking phenomena during numerical computation of {S}chwarz-{C}hristoffel conformal transformations",
JOURNAL=MOTL,
VOLUME=20,
NUMBER=4,
PAGES={223--225},
MONTH=FEB,
YEAR=1999}


*** Analisi numerica

@ARTICLE{Shanks,
AUTHOR="D. Shanks",
TITLE="Non-linear transformations of divergent and slowly convergent
sequences",
JOURNAL=JM&P,
VOLUME=34,
PAGES={1--42},
YEAR=1955}

@ARTICLE{Wynn-1,
AUTHOR="P. Wynn",
TITLE="On a Device for Computing the {$e_m(S_n)$} Transformation",
JOURNAL=MTAC,
VOLUME=10,
PAGES={91--96},
YEAR=1956}

@ARTICLE{Dingle-2,
AUTHOR="R. B. Dingle",
TITLE="The {B}ose-{E}instein Integrals {${\cal B}_{p}(\eta) = (p!)^{-1} \int_{0}^{\infty}\epsilon^{p}(\mathrm{e}^{\epsilon-\eta}-1)^{-1} \mathrm{d}\epsilon$}",
JOURNAL=ASRB,
VOLUME=6,
PAGES={240--252},
YEAR=1957}

@ARTICLE{Di-Ar-Ro-1,
AUTHOR="R. B. Dingle and D. Arndt and S. K. Roy",
TITLE="The Integrals {${\cal U}_{p}(x) = (p!)^{-1}\int_{0}^{\infty}\epsilon^{p} (\epsilon+x)^{-1}\mathrm{e}^{-\epsilon}\mathrm{d}\epsilon$} and {${\cal B}_{p}(x)=(p!)^{-1}\int_{0}^{\infty}\epsilon^{p} (\epsilon+x)^{-2}\mathrm{e}^{-\epsilon}\mathrm{d}\epsilon$} and Their Tabulation",
JOURNAL=ASRB,
VOLUME=6,
PAGES={144--154},
YEAR=1957}

@ARTICLE{Di-Ar-Ro-2,
AUTHOR="R. B. Dingle and D. Arndt and S. K. Roy",
TITLE="The Integrals {${\cal C}_{p}(x) = (p!)^{-1}\int_{0}^{\infty}\epsilon^{p} (\epsilon^2+x^2)^{-1}\mathrm{e}^{-\epsilon}\mathrm{d}\epsilon$} and {${\cal D}_{p}(x)=(p!)^{-1}\int_{0}^{\infty}\epsilon^{p} (\epsilon^2+x^2)^{-2}\mathrm{e}^{-\epsilon}\mathrm{d}\epsilon$} and Their Tabulation",
JOURNAL=ASRB,
VOLUME=6,
PAGES={155--164},
YEAR=1957}

@ARTICLE{Di-Ar-Ro-3,
AUTHOR="R. B. Dingle and D. Arndt and S. K. Roy",
TITLE="The Integrals {${\cal C}_{p}(x) = (p!)^{-1}\int_{0}^{\infty}\epsilon^{p} (1+x\epsilon^3)^{-1}\mathrm{e}^{-\epsilon}\mathrm{d}\epsilon$} and {${\cal F}_{p}(x)=(p!)^{-1}\int_{0}^{\infty}\epsilon^{p} (1+x\epsilon^3)^{-2}\mathrm{e}^{-\epsilon}\mathrm{d}\epsilon$} and Their Tabulation",
JOURNAL=ASRB,
VOLUME=6,
PAGES={245--252},
YEAR=1957}

@ARTICLE{Dingle-3,
AUTHOR="R. B. Dingle",
TITLE="Asymptotic expansions and converging factors {I}. {G}eneral theory and basic converging factors",
JOURNAL=PRSLA,
VOLUME=244,
PAGES={456--475},
YEAR=1958}

@ARTICLE{Dingle-4,
AUTHOR="R. B. Dingle",
TITLE="Asymptotic expansions and converging factors {II}. {E}rror, {D}awson, {F}resnel, exponential, sine and cosine, and similar integrals",
JOURNAL=PRSLA,
VOLUME=244,
PAGES={476--483},
YEAR=1958}

@ARTICLE{Wynn-2,
AUTHOR="P. Wynn",
TITLE="The Rational Approximation of Functions which Are Formally Defined by a Power Series Expansion",
JOURNAL=MC,
VOLUME=14,
PAGES={147--186},
YEAR=1960}

@ARTICLE{Thacher,
AUTHOR="Thacher, Jr., H. C.",
TITLE="Algorithm 215: {SHANKS}",
JOURNAL=CACM,
VOLUME=6,
PAGES=662,
MONTH=NOV,
YEAR=1963}

@ARTICLE{Ga-He,
AUTHOR="I. Gargantini and P. Henrici",
TITLE="A Continued Fraction Algorithm for the Computation of Higher Transcendental Functions in the Complex Plane",
JOURNAL=MC,
VOLUME=21,
NUMBER=97,
PAGES={18--29},
YEAR=1967}

@ARTICLE{Ol-So,
AUTHOR="F. W. J. Olver and D. J. Sookne",
TITLE="Note on Backward Recurrence Algorithms",
JOURNAL=MC,
VOLUME=26,
NUMBER=120,
PAGES={941--947},
MONTH=OCT,
YEAR=1972}

@ARTICLE{Levin,
AUTHOR="D. Levin",
TITLE="Development of Non-Linear Transformations for Improving
Convergence of Sequences",
JOURNAL=IJCMB,
VOLUME=3,
NUMBER=4,
PAGES={371--388},
YEAR=1973}

@ARTICLE{Jo-Th,
AUTHOR="W. B. Jones and W. J. Thron",
TITLE="Numerical Stability in Evaluating Continued Fractions",
JOURNAL=MC,
VOLUME=28,
NUMBER=127,
PAGES={795--810},
MONTH=JUL,
YEAR=1974}

@ARTICLE{McCabe,
AUTHOR="J. H. McCabe",
TITLE="A Continued Fraction Expansion, with a Truncation Error Estimate, for {D}awson's Integral",
JOURNAL=MC,
VOLUME=28,
NUMBER=127,
PAGES={811--816},
MONTH=JUL,
YEAR=1974}

@ARTICLE{Temme-1,
AUTHOR="N. M. Temme",
TITLE="Uniform Asymptotic Expansions of the Incomplete Gamma Functions and the Incomplete Beta Functions",
JOURNAL=MC,
VOLUME=29,
NUMBER=132,
PAGES={1109--1114},
MONTH=OCT,
YEAR=1975}

@ARTICLE{Co-Je,
AUTHOR="R. B. Corr and A. Jennings",
TITLE="A Simultaneous Iteration Algorithm for Symmetric Eigenvalue Problems",
JOURNAL=IJNME,
VOLUME=10,
PAGES={647--663},
YEAR=1976}

@ARTICLE{Fo-Ha-Sc,
AUTHOR="P. A. Fox and A. D. Hall and N. L. Schryer",
TITLE="Algorithm 528. {F}ramework for a Portable Library",
JOURNAL=ACMMS,
VOLUME=4,
NUMBER=2,
PAGES={177--188},
MONTH=JUN,
YEAR=1978}

@ARTICLE{Sidi-1,
AUTHOR="A. Sidi",
TITLE="Convergence Properties of Some Nonlinear Sequence Transformations",
JOURNAL=MC,
VOLUME=33,
NUMBER=145,
PAGES={315--326},
MONTH=JAN,
YEAR=1979}

@ARTICLE{Sm-Fo-1,
AUTHOR="D. A. Smith and W. F. Ford",
TITLE="Acceleration of Linear and Logarithmic Convergence",
JOURNAL=SIAMN,
VOLUME=16,
NUMBER=2,
PAGES={223--240},
MONTH=APR,
YEAR=1979}

@ARTICLE{King,
AUTHOR="R. F. King",
TITLE="An Extrapolation Method of Order Four for Linear Sequences",
JOURNAL=SIAMN,
VOLUME=16,
NUMBER=5,
PAGES={719--725},
MONTH=OCT,
YEAR=1979}

@ARTICLE{Gautschi-2,
AUTHOR="W. Gautschi",
TITLE="A Computational Procedure for Incomplete Gamma Functions",
JOURNAL=ACMMS,
VOLUME=5,
NUMBER=4,
PAGES={466--481},
MONTH=DEC,
YEAR=1979}

@ARTICLE{Gautschi-3,
AUTHOR="W. Gautschi",
TITLE="Algorithm 542. {I}ncomplete Gamma Functions",
JOURNAL=ACMMS,
VOLUME=5,
NUMBER=4,
PAGES={482--489},
MONTH=DEC,
YEAR=1979}

@ARTICLE{Philip,
AUTHOR="J. R. Philip",
TITLE="The Convergence and Partial Convergence of Alternating Series",
JOURNAL=MC,
VOLUME=35,
NUMBER=151,
PAGES={907--916},
MONTH=JUL,
YEAR=1980}

@ARTICLE{Sidi-2,
AUTHOR="A. Sidi",
TITLE="Analysis of Convergence of the {$T$}-Transformation for Power Series",
JOURNAL=MC,
VOLUME=35,
NUMBER=151,
PAGES={833--850},
MONTH=JUL,
YEAR=1980}

@ARTICLE{As-Ch-Ru-1,
AUTHOR="U. Ascher and J. Christiansen and R. D. Russel",
TITLE="Collocation Software for Boundary-Value {ODEs}",
JOURNAL=ACMMS,
VOLUME=7,
NUMBER=2,
PAGES={209--222},
MONTH=JUN,
YEAR=1981}

@ARTICLE{As-Ch-Ru-2,
AUTHOR="U. Ascher and J. Christiansen and R. D. Russel",
TITLE="Algorithm 569. {COLSYS}: {C}ollocation Software for Boundary-Value {ODEs}",
JOURNAL=ACMMS,
VOLUME=7,
NUMBER=2,
PAGES={223--229},
MONTH=JUN,
YEAR=1981}

@ARTICLE{Ma-Jo,
AUTHOR="Marshall Ash, J. and R. L. Jones",
TITLE="Optimal Numerical Differentiation Using Three Function Evaluations",
JOURNAL=MC,
VOLUME=37,
NUMBER=155,
PAGES={159--167},
MONTH=JUL,
YEAR=1981}

@ARTICLE{Brezinski-2,
AUTHOR="C. Brezinski",
TITLE="Some New Convergence Acceleration Methods",
JOURNAL=MC,
VOLUME=39,
NUMBER=159,
PAGES={133--145},
MONTH=JUL,
YEAR=1982}

@ARTICLE{Brezinski-3,
AUTHOR="C. Brezinski",
TITLE="Algorithm 585. {A} Subroutine for the General Interpolation and Extrapolation Problems",
JOURNAL=ACMMS,
VOLUME=8,
NUMBER=3,
PAGES={290--301},
MONTH=SEP,
YEAR=1982}

@ARTICLE{Sm-Fo-2,
AUTHOR="D. A. Smith and W. F. Ford",
TITLE="Numerical Comparisons of Nonlinear Convergence Accelerators",
JOURNAL=MC,
VOLUME=38,
PAGES={481--499},
YEAR=1982}

@ARTICLE{Cody-1,
AUTHOR="W. J. Cody",
TITLE="Algorithm 597. {S}equence of Modified {B}essel Functions of the First Kind",
JOURNAL=ACMMS,
VOLUME=9,
NUMBER=2,
PAGES={242--245},
MONTH=JUN,
YEAR=1983}

@ARTICLE{Si-Le,
AUTHOR="A. Sidi and D. Levin",
TITLE="Prediction Properties of the $t$-Transformation",
JOURNAL=SIAMN,
VOLUME=20,
NUMBER=3,
PAGES={589--598},
MONTH=JUN,
YEAR=1983}

@ARTICLE{Fe-Fo-Sm-1,
AUTHOR="T. Fessler and W. F. Ford and D. A. Smith",
TITLE="{HURRY}: {A}n Acceleration Algorithm for Scalar Sequences and Series",
JOURNAL=ACMMS,
VOLUME=9,
NUMBER=3,
PAGES={346--354},
MONTH=SEP,
YEAR=1983}

@ARTICLE{Fe-Fo-Sm-2,
AUTHOR="T. Fessler and W. F. Ford and D. A. Smith",
TITLE="Algorithm 602. {HURRY}: {A}n Acceleration Algorithm for Scalar
Sequences and Series",
JOURNAL=ACMMS,
VOLUME=9,
NUMBER=3,
PAGES={355--357},
MONTH=SEP,
YEAR=1983}

@ARTICLE{Br-De-Ge,
AUTHOR="C. Brezinski and J. P. Delahaye and B. Germain-Bonne",
TITLE="Convergence Acceleration by Extraction of Linear Subsequences",
JOURNAL=SIAMN,
VOLUME=20,
NUMBER=6,
PAGES={1099--1105},
MONTH=DEC,
YEAR=1983}

@ARTICLE{Ri-Ha,
AUTHOR="J. R. Rice and R. J. Hanson",
TITLE="References and Keywords for {\emph{Collected Algorithms from ACM}}",
JOURNAL=ACMMS,
VOLUME=10,
NUMBER=4,
PAGES={359--360},
MONTH=DEC,
YEAR=1984}

@ARTICLE{Amos,
AUTHOR="D. E. Amos",
TITLE="Algorithm 644. {A} Portable Package for {B}essel Functions of a
Complex Argument and Nonnegative Order",
JOURNAL=ACMMS,
VOLUME=12,
NUMBER=3,
PAGES={265--273},
MONTH=SEP,
YEAR=1986}

@ARTICLE{Di-Mo-1,
AUTHOR="A. R. DiDonato and Morris, Jr., A. H.",
TITLE="Computation of the Incomplete Gamma Function Ratios and their
Inverse",
JOURNAL=ACMMS,
VOLUME=12,
NUMBER=4,
PAGES={377--393},
MONTH=DEC,
YEAR=1986}

@ARTICLE{Di-Mo-2,
AUTHOR="A. R. DiDonato and Morris, Jr., A. H.",
TITLE="Algorithm 654. {FORTRAN} Subroutines for Computing the Incomplete
Gamma Function Ratios and their Inverse",
JOURNAL=ACMMS,
VOLUME=13,
NUMBER=3,
PAGES={318--319},
MONTH=SEP,
YEAR=1987}

@ARTICLE{Fo-Si,
AUTHOR="W. F. Ford and A. Sidi",
TITLE="An Algorithm for a Generalization of the {R}ichardson
Extrapolation Process",
JOURNAL=SIAMN,
VOLUME=24,
NUMBER=5,
PAGES={1212--1232},
MONTH=OCT,
YEAR=1987}

@ARTICLE{Basrak,
AUTHOR="Z. Basrak",
TITLE="A Routine for Parameter Optimization Using an Accelerated
Grid-Search Method",
JOURNAL=CPC,
VOLUME=46,
PAGES={149--154},
YEAR=1987}

@ARTICLE{Cody-2,
AUTHOR="W. J. Cody",
TITLE="Algorithm 665. {MACHAR}: {A} Subroutine to Dynamically Determine
Machine Parameters",
JOURNAL=ACMMS,
VOLUME=14,
NUMBER=4,
PAGES={303--311},
MONTH=DEC,
YEAR=1988}

@ARTICLE{Osada,
AUTHOR="N. Osada",
TITLE="A Convergence Acceleration Method for some Logarithmically
Convergent Sequences",
JOURNAL=SIAMN,
VOLUME=27,
NUMBER=1,
PAGES={178--189},
MONTH=FEB,
YEAR=1990}

@ARTICLE{Si-Si-1,
AUTHOR="S. Singh and R. Singh",
TITLE="Application of Transforms to Accelerate the Summation of Periodic
Free-Space {G}reen's Functions",
JOURNAL=TMTT,
VOLUME={MTT-38},
NUMBER=11,
PAGES={1746--1748},
MONTH=NOV,
YEAR=1990}

@ARTICLE{Si-Ri-Zi-Wi,
AUTHOR="S. Singh and W. F. Richards and J. R. Zinecker and D. R.
Wilton",
TITLE="Accelerating the Convergence of Series Representing the
Free-Space Periodic {G}reen's Function",
JOURNAL=TAP,
VOLUME={AP-38},
NUMBER=12,
PAGES={1958--1962},
MONTH=DEC,
YEAR=1990}

@ARTICLE{Si-Si-2,
AUTHOR="S. Singh and R. Singh",
TITLE="On the Use of {S}hanks's Transform to Accelerate the Summation of
Slowly Converging Series",
JOURNAL=TMTT,
VOLUME={MTT-39},
NUMBER=3,
PAGES={608--610},
MONTH=MAR,
YEAR=1991}

@ARTICLE{Fa-Lo-Ro,
AUTHOR="P. Favati and G. Lotti and F. Romani",
TITLE="Algorithm 691. {I}mproving {QUADPACK} Automatic Integration
Routines",
JOURNAL=ACMMS,
VOLUME=17,
NUMBER=2,
PAGES={218--232},
MONTH=JUN,
YEAR=1991}

@ARTICLE{Gautschi-4,
AUTHOR="W. Gautschi",
TITLE="A Class of Slowly Convergent Series and Their Summmation by
{G}aussian Quadrature",
JOURNAL=MC,
VOLUME=57,
NUMBER=195,
PAGES={309--324},
MONTH=JUL,
YEAR=1991}

@ARTICLE{Gautschi-5,
AUTHOR="W. Gautschi",
TITLE="On Certain Slowly Convergent Series Occurring in Plate Contact
Problems",
JOURNAL=MC,
VOLUME=57,
NUMBER=195,
PAGES={325--338},
MONTH=JUL,
YEAR=1991}

@ARTICLE{Temme-2,
AUTHOR="N. M. Temme",
TITLE="Asymptotic Inversion of Incomplete Gamma Functions",
JOURNAL=MC,
VOLUME=58,
NUMBER=198,
PAGES={755--764},
MONTH=APR,
YEAR=1992}

@ARTICLE{Na-Pe-Bh,
AUTHOR="M. Nardin and W. F. Perger and A. Bhalla",
TITLE="Algorithm 707. {CONHYP}: {A} Numerical Evaluator of the Confluent
Hypergeometric Function for Complex Argument of Large Magnitudes",
JOURNAL=ACMMS,
VOLUME=18,
NUMBER=3,
PAGES={345--349},
MONTH=SEP,
YEAR=1992}

@ARTICLE{Si-Si-3,
AUTHOR="S. Singh and R. Singh",
TITLE="On Improving the Computational Efficiency in Problems Involving One- and Two-Dimensional Periodicity",
JOURNAL=JEWA,
VOLUME=6,
NUMBER=7,
PAGES={911--919},
YEAR=1992}

@ARTICLE{96Morgan_MC,
AUTHOR="R. B. Morgan",
TITLE="On Restarting the {A}rnoldi Method for Large Nonsymmetric Eigenvalue Problems",
JOURNAL=MC,
VOLUME=65,
NUMBER=215,
PAGES={1213--1230},
MONTH=JUL,
YEAR=1996}

@ARTICLE{96Lehoucq_SIAMM,
AUTHOR="R. B. Lehoucq and D. C. Sorensen",
TITLE="Deflation Techniques for an Implicitly Restarted {A}rnoldi Iteration",
JOURNAL=SIAMM,
VOLUME=17,
NUMBER=4,
PAGES={789--821},
YEAR=1996}

@ARTICLE{97Meerbergen_MC,
AUTHOR="K. Meerbergen and A. Spence",
TITLE="Implicitly Restarted {A}rnoldi with Purification for the Shift-Invert Transformation",
JOURNAL=MC,
VOLUME=66,
NUMBER=218,
PAGES={667--689},
MONTH=APR,
YEAR=1997}

@ARTICLE{00Dassie_MC,
AUTHOR="S. Dassi{\`e} and M. Vianello and R. Zanovello",
TITLE="A New Summation Method for Power Series with Rational Coefficients",
JOURNAL=MC,
VOLUME=69,
NUMBER=230,
PAGES={749--756},
YEAR=2000}

@ARTICLE{2012Spandaw_RJ,
DOI={10.1007/s11139-011-9353-7},
AUTHOR="Jeroen Spandaw and van Straten, Duco",
TITLE="Hyperelliptic integrals and generalized arithmetic-geometric mean",
JOURNAL=RJ,
VOLUME=28,
PAGES={61--78},
YEAR=2012}


*** Computing

@ARTICLE{72Flynn_TOC,
AUTHOR="M. J. Flynn",
TITLE="Some Computer Organizations and Their Effectiveness",
JOURNAL=TOC,
VOLUME={C-21},
NUMBER=9,
PAGES={948--960},
MONTH=SEP,
YEAR=1972}
