generalized%20exponential%20integrals
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11—20 of 21 matching pages
11: 11.6 Asymptotic Expansions
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11.6.3
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11.6.5
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βΊMore fully, the series (11.2.1) and (11.2.2) can be regarded as generalized asymptotic expansions (§2.1(v)).
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12: Bibliography G
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On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
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Algorithm 471: Exponential integrals.
Comm. ACM 16 (12), pp. 761–763.
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Exponential integral
for large values of
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J. Res. Nat. Bur. Standards 62, pp. 123–125.
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On the computation of generalized Fermi-Dirac and Bose-Einstein integrals.
Comput. Phys. Comm. 74 (2), pp. 233–238.
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A table of integrals of the exponential integral.
J. Res. Nat. Bur. Standards Sect. B 73B, pp. 191–210.
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13: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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The efficient computation of some generalised exponential integrals.
J. Comput. Appl. Math. 148 (2), pp. 363–374.
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The exponential integral distribution.
Statist. Probab. Lett. 5 (3), pp. 209–211.
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The generalized integro-exponential function.
Math. Comp. 44 (170), pp. 443–458.
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Tables of Generalized Exponential Integrals.
NPL Mathematical Tables, Vol. III, Her Majesty’s Stationery Office, London.
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14: 36.5 Stokes Sets
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βΊThe Stokes sets are defined by the exponential dominance condition:
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§36.5(ii) Cuspoids
… βΊThey generate a pair of cusp-edged sheets connected to the cusped sheets of the swallowtail bifurcation set (§36.4). … βΊThe first sheet corresponds to and is generated as a solution of Equations (36.5.6)–(36.5.9). … βΊ§36.5(iv) Visualizations
…15: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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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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16: Bibliography V
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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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Generalized Associated Legendre Functions and their Applications.
World Scientific Publishing Co. Inc., Singapore.
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A note on the asymptotic expansion of generalized hypergeometric functions.
Anal. Appl. (Singap.) 12 (1), pp. 107–115.
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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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17: 20.11 Generalizations and Analogs
§20.11 Generalizations and Analogs
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20.11.1
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20.11.2
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βΊWith the substitutions , , with , we have
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βΊAs in §20.11(ii), the modulus of elliptic integrals (§19.2(ii)), Jacobian elliptic functions (§22.2), and Weierstrass elliptic functions (§23.6(ii)) can be expanded in -series via (20.9.1).
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18: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Generalized Fermi-Dirac integrals—FD, FDG, FDH.
Comput. Phys. Comm. 39 (2), pp. 181–185.
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19: Bibliography W
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Caustics: Mathematical curves generated by light shined through rippled plastic.
Scientific American 249, pp. 146–153.
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Infinitely differentiable generalized logarithmic and exponential functions.
Math. Comp. 57 (196), pp. 723–733.
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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 transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 26 (2), pp. 257–272.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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20: Bibliography P
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Algorithm 385: Exponential integral
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Comm. ACM 13 (7), pp. 446–447.
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Tables of the Exponential Integral
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Pergamon Press, New York.
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Exponential asymptotics of the Mittag-Leffler function.
Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
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Numerical calculation of the generalized Fermi-Dirac integrals.
Comput. Phys. Comm. 55 (2), pp. 127–136.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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