relations%20to%20exponential%20integrals
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11—18 of 18 matching pages
11: Bibliography C
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Table of integrals of squared Jacobian elliptic functions and reductions of related hypergeometric -functions.
Math. Comp. 75 (255), pp. 1309–1318.
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A numerical method for generalized exponential integrals.
Comput. Math. Appl. 14 (4), pp. 261–268.
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On the evaluation of generalized exponential integrals
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J. Comput. Phys. 78 (2), pp. 278–287.
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Performance evaluation of programs related to the real gamma function.
ACM Trans. Math. Software 17 (1), pp. 46–54.
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Applications of the complex exponential integral.
Math. Comp. 15 (73), pp. 1–6.
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12: Bibliography D
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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory.
Comm. Pure Appl. Math. 52 (11), pp. 1335–1425.
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Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities.
Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.
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Error analysis in a uniform asymptotic expansion for the generalised exponential integral.
J. Comput. Appl. Math. 80 (1), pp. 127–161.
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Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
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The Legendre Relation for Elliptic Integrals.
In Paul Halmos: Celebrating 50 Years of Mathematics, J. H. Ewing and F. W. Gehring (Eds.),
pp. 305–315.
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13: Bibliography S
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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations.
SIAM J. Math. Anal. 10 (4), pp. 823–838.
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Structure of avoided crossings for eigenvalues related to equations of Heun’s class.
J. Phys. A 30 (2), pp. 673–687.
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Integral equations and relations for Lamé functions and ellipsoidal wave functions.
Proc. Cambridge Philos. Soc. 64, pp. 113–126.
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Algorithm 911: multiple-precision exponential integral and related functions.
ACM Trans. Math. Software 37 (4), pp. Art. 46, 16.
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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions.
J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.
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14: Bibliography V
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An integral transform involving Heun functions and a related eigenvalue problem.
SIAM J. Math. Anal. 17 (3), pp. 688–703.
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Calculation of Special Functions: The Gamma Function, the Exponential Integrals and Error-Like Functions.
CWI Tract, Vol. 10, Stichting Mathematisch Centrum, Centrum voor Wiskunde en
Informatica, Amsterdam.
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Rational approximations for exponential integrals
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Acad. Roy. Belg. Bull. Cl. Sci. (5) 56, pp. 1064–1072.
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Integral relations for Lamé functions.
SIAM J. Math. Anal. 13 (6), pp. 978–987.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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15: 14.30 Spherical and Spheroidal Harmonics
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and () are often referred to as the prolate spheroidal harmonics of the first and second kinds, respectively.
…Segura and Gil (1999) introduced the scaled oblate spheroidal harmonics and which are real when and .
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14.30.3
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►See also (34.3.22), and for further related integrals see Askey et al. (1986).
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14.30.8_5
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16: Bibliography W
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Some useful integrals of
and related integrals.
Optica Acta 14 (3), pp. 317–322.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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Computation with Recurrence Relations.
Pitman, Boston, MA.
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17: Bibliography O
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Summing one- and two-dimensional series related to the Euler series.
J. Comput. Appl. Math. 98 (2), pp. 245–271.
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Asymptotic expansions for -gamma, -exponential, and -Bessel functions.
J. Math. Anal. Appl. 186 (3), pp. 896–913.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral.
SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
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The Generalized Exponential Integral.
In Approximation and Computation (West Lafayette, IN, 1993), R. V. M. Zahar (Ed.),
International Series of Numerical Mathematics, Vol. 119, pp. 497–510.
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18: 36.5 Stokes Sets
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►The Stokes sets are defined by the exponential dominance condition:
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