-
B. Gabutti and G. Allasia (2008)
Evaluation of
-gamma function and
-analogues by iterative algorithms,
Numer. Algorithms 49 (1-4), pp. 159–168.
-
B. Gabutti and B. Minetti (1981)
A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function,
J. Comput. Phys. 42 (2), pp. 277–287.
-
B. Gabutti (1979)
On high precision methods for computing integrals involving Bessel functions,
Math. Comp. 33 (147), pp. 1049–1057.
-
B. Gabutti (1980)
On the generalization of a method for computing Bessel function integrals,
J. Comput. Appl. Math. 6 (2), pp. 167–168.
-
B. Gambier (1910)
Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes,
Acta Math. 33 (1), pp. 1–55.
-
GAP (Web Site)
The GAP Group, Centre for Interdisciplinary Research in Computational Algebra,
University of St. Andrews, United Kingdom..
-
I. Gargantini and P. Henrici (1967)
A continued fraction algorithm for the computation of higher transcendental functions in the complex plane,
Math. Comp. 21 (97), pp. 18–29.
-
G. Gasper and M. Rahman (2004)
Basic Hypergeometric Series,
Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.
-
G. Gasper (1972)
An inequality of Turán type for Jacobi polynomials,
Proc. Amer. Math. Soc. 32, pp. 435–439.
-
G. Gasper (1975)
Formulas of the Dirichlet-Mehler Type,
in Fractional Calculus and its Applications,
Lecture Notes in Math., Vol. 457, pp. 207–215.
-
G. Gasper (1981)
Orthogonality of certain functions with respect to complex valued weights,
Canad. J. Math. 33 (5), pp. 1261–1270.
-
L. Gatteschi (1987)
New inequalities for the zeros of Jacobi polynomials,
SIAM J. Math. Anal. 18 (6), pp. 1549–1562.
-
L. Gatteschi (1990)
New inequalities for the zeros of confluent hypergeometric functions,
in Asymptotic and computational analysis (Winnipeg, MB, 1989),
pp. 175–192.
-
L. Gatteschi (2002)
Asymptotics and bounds for the zeros of Laguerre polynomials: A survey,
J. Comput. Appl. Math. 144 (1-2), pp. 7–27.
-
M. Gaudin (1983)
La fonction d’onde de Bethe,
Masson, Paris (French).
-
J. A. Gaunt (1929)
The triplets of helium,
Philos. Trans. Roy. Soc. London Ser. A 228, pp. 151–196.
-
C. F. Gauss (1863)
Werke. Band II,
pp. 436–447 (German).
-
W. Gautschi (1964a)
Algorithm 222: Incomplete beta function ratios,
Comm. ACM 7 (3), pp. 143–144.
-
W. Gautschi (1964b)
Algorithm 236: Bessel functions of the first kind,
Comm. ACM 7 (8), pp. 479–480.
-
W. Gautschi (1965)
Algorithm 259: Legendre functions for arguments larger than one,
Comm. ACM 8 (8), pp. 488–492.
-
W. Gautschi (1966)
Algorithm 292: Regular Coulomb wave functions,
Comm. ACM 9 (11), pp. 793–795.
-
W. Gautschi (1969)
Algorithm 363: Complex error function,
Comm. ACM 12 (11), pp. 635.
-
W. Gautschi (1973)
Algorithm 471: Exponential integrals,
Comm. ACM 16 (12), pp. 761–763.
-
W. Gautschi (1977a)
Evaluation of the repeated integrals of the coerror function,
ACM Trans. Math. Software 3, pp. 240–252.
-
W. Gautschi (1977b)
Algorithm 521: Repeated integrals of the coerror function,
ACM Trans. Math. Software 3, pp. 301–302.
-
W. Gautschi (1979a)
Algorithm 542: Incomplete gamma functions,
ACM Trans. Math. Software 5 (4), pp. 482–489.
-
W. Gautschi (1994)
Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules,
ACM Trans. Math. Software 20 (1), pp. 21–62.
-
W. Gautschi and J. Slavik (1978)
On the computation of modified Bessel function ratios,
Math. Comp. 32 (143), pp. 865–875.
-
W. Gautschi (1959a)
Exponential integral
for large values of 
,
J. Res. Nat. Bur. Standards 62, pp. 123–125.
-
W. Gautschi (1959b)
Some elementary inequalities relating to the gamma and incomplete gamma function,
J. Math. Phys. 38 (1), pp. 77–81.
-
W. Gautschi (1961)
Recursive computation of the repeated integrals of the error function,
Math. Comp. 15 (75), pp. 227–232.
-
W. Gautschi (1967)
Computational aspects of three-term recurrence relations,
SIAM Rev. 9 (1), pp. 24–82.
-
W. Gautschi (1970)
Efficient computation of the complex error function,
SIAM J. Numer. Anal. 7 (1), pp. 187–198.
-
W. Gautschi (1974)
A harmonic mean inequality for the gamma function,
SIAM J. Math. Anal. 5 (2), pp. 278–281.
-
W. Gautschi (1975)
Computational Methods in Special Functions – A Survey,
in Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975),
pp. 1–98. Math. Res. Center, Univ. Wisconsin Publ., No. 35.
-
W. Gautschi (1979b)
A computational procedure for incomplete gamma functions,
ACM Trans. Math. Software 5 (4), pp. 466–481.
-
W. Gautschi (1979c)
Un procedimento di calcolo per le funzioni gamma incomplete,
Rend. Sem. Mat. Univ. Politec. Torino 37 (1), pp. 1–9 (Italian).
-
W. Gautschi (1983)
How and how not to check Gaussian quadrature formulae,
BIT 23 (2), pp. 209–216.
-
W. Gautschi (1984)
Questions of Numerical Condition Related to Polynomials,
in Studies in Numerical Analysis,
pp. 140–177.
-
W. Gautschi (1993)
On the computation of generalized Fermi-Dirac and Bose-Einstein integrals,
Comput. Phys. Comm. 74 (2), pp. 233–238.
-
W. Gautschi (1996)
Orthogonal Polynomials: Applications and Computation,
in Acta Numerica, 1996,
Acta Numerica, Vol. 5, pp. 45–119.
-
W. Gautschi (1997a)
Numerical Analysis. An Introduction,
Birkhäuser Boston Inc., Boston, MA.
-
W. Gautschi (1997b)
The Computation of Special Functions by Linear Difference Equations,
in Advances in Difference Equations (Veszprém, 1995),
(I. Győri and G. Ladas Eds.), pp. 213–243.
-
W. Gautschi (1998)
The incomplete gamma functions since Tricomi,
in Tricomi’s Ideas and Contemporary Applied Mathematics
(Rome/Turin, 1997),
Atti Convegni Lincei, Vol. 147, pp. 203–237.
-
W. Gautschi (1999)
A note on the recursive calculation of incomplete gamma functions,
ACM Trans. Math. Software 25 (1), pp. 101–107.
-
W. Gautschi (2002a)
Computation of Bessel and Airy functions and of related Gaussian quadrature formulae,
BIT 42 (1), pp. 110–118.
-
W. Gautschi (2002b)
Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions,
J. Comput. Appl. Math. 139 (1), pp. 173–187.
-
W. Gautschi (2004)
Orthogonal Polynomials: Computation and Approximation,
Numerical Mathematics and Scientific Computation, Oxford University Press, New York.
-
M. Gavrila (1967)
Elastic scattering of photons by a hydrogen atom,
Phys. Rev. 163 (1), pp. 147–155.
-
M. Geller and E. W. Ng (1969)
A table of integrals of the exponential integral,
J. Res. Nat. Bur. Standards Sect. B 73B, pp. 191–210.
-
M. Geller and E. W. Ng (1971)
A table of integrals of the error function. II. Additions and corrections,
J. Res. Nat. Bur. Standards Sect. B 75B, pp. 149–163.
-
I. M. Gel’fand and G. E. Shilov (1964)
Generalized Functions. Vol. 1: Properties and Operations,
Academic Press, New York.
-
K. Germey (1964)
Die Beugung einer ebenen elektromanetischen Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt,
Ann. Physik (7) 468, pp. 237–251 (German).
-
J. S. Geronimo, O. Bruno and W. Van Assche (2004)
WKB and turning point theory for second-order difference equations,
in Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
-
A. Gervois and H. Navelet (1984)
Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities,
J. Math. Phys. 25 (11), pp. 3350–3356.
-
A. Gervois and H. Navelet (1985a)
Integrals of three Bessel functions and Legendre functions. I,
J. Math. Phys. 26 (4), pp. 633–644.
-
A. Gervois and H. Navelet (1985b)
Integrals of three Bessel functions and Legendre functions. II,
J. Math. Phys. 26 (4), pp. 645–655.
-
A. Gervois and H. Navelet (1986a)
Some integrals involving three modified Bessel functions. I,
J. Math. Phys. 27 (3), pp. 682–687.
-
A. Gervois and H. Navelet (1986b)
Some integrals involving three modified Bessel functions. II,
J. Math. Phys. 27 (3), pp. 688–695.
-
I. M. Gessel (2003)
Applications of the classical umbral calculus,
Algebra Universalis 49 (4), pp. 397–434.
-
P. Gianni, M. Seppälä, R. Silhol and B. Trager (1998)
Riemann surfaces, plane algebraic curves and their period matrices,
J. Symbolic Comput. 26 (6), pp. 789–803.
-
A. G. Gibbs (1973)
Problem 72-21, Laplace transforms of Airy functions,
SIAM Rev. 15 (4), pp. 796–798.
-
A. Gil and J. Segura (1997)
Evaluation of Legendre functions of argument greater than one,
Comput. Phys. Comm. 105 (2-3), pp. 273–283.
-
A. Gil and J. Segura (1998)
A code to evaluate prolate and oblate spheroidal harmonics,
Comput. Phys. Comm. 108 (2-3), pp. 267–278.
-
A. Gil and J. Segura (2000)
Evaluation of toroidal harmonics,
Comput. Phys. Comm. 124 (1), pp. 104–122.
-
A. Gil and J. Segura (2001)
DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics,
Comput. Phys. Comm. 139 (2), pp. 186–191.
-
A. Gil, J. Segura and N. M. Temme (2000)
Computing toroidal functions for wide ranges of the parameters,
J. Comput. Phys. 161 (1), pp. 204–217.
-
A. Gil, J. Segura and N. M. Temme (2001)
On nonoscillating integrals for computing inhomogeneous Airy functions,
Math. Comp. 70 (235), pp. 1183–1194.
-
A. Gil, J. Segura and N. M. Temme (2002a)
Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions,
ACM Trans. Math. Software 28 (3), pp. 325–336.
-
A. Gil, J. Segura and N. M. Temme (2002b)
Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions,
ACM Trans. Math. Software 28 (4), pp. 436–447.
-
A. Gil, J. Segura and N. M. Temme (2002c)
Computing complex Airy functions by numerical quadrature,
Numer. Algorithms 30 (1), pp. 11–23.
-
A. Gil, J. Segura and N. M. Temme (2002d)
Evaluation of the modified Bessel function of the third kind of imaginary orders,
J. Comput. Phys. 175 (2), pp. 398–411.
-
A. Gil, J. Segura and N. M. Temme (2003a)
Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion,
J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
-
A. Gil, J. Segura and N. M. Temme (2003b)
Computing special functions by using quadrature rules,
Numer. Algorithms 33 (1-4), pp. 265–275.
-
A. Gil, J. Segura and N. M. Temme (2003c)
On the zeros of the Scorer functions,
J. Approx. Theory 120 (2), pp. 253–266.
-
A. Gil, J. Segura and N. M. Temme (2004a)
Algorithm 831: Modified Bessel functions of imaginary order and positive argument,
ACM Trans. Math. Software 30 (2), pp. 159–164.
-
A. Gil, J. Segura and N. M. Temme (2004b)
Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments,
ACM Trans. Math. Software 30 (2), pp. 145–158.
-
A. Gil, J. Segura and N. M. Temme (2004c)
Integral representations for computing real parabolic cylinder functions,
Numer. Math. 98 (1), pp. 105–134.
-
A. Gil, J. Segura and N. M. Temme (2006a)
Computing the real parabolic cylinder functions
, 
,
ACM Trans. Math. Software 32 (1), pp. 70–101.