Integrals involving E-functions
Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 186-187
Voir la notice de l'article provenant de la source Cambridge University Press
In this paper three integrals involving E-functions are evaluated in terms of E-functions. The formulae to be established are:where n is a positive integer, | args z < π, R(γ ± m ÷ 1⁄2) > 0, αρ+ν = (2γ + ν)/2n (ν = 1, 2, ..., 2n), αρ+2n+i = (γ + m - 1⁄2 + i)/n, αρ+3n+i = (γ - m - 1⁄2 + i)/n, βα+i = (γ + κ + i)/n, βα+ν+i = (γ - κ + i)/n(i = 1, 2, ..., n).where n is a positive integer, |arg z| < π, R(λ±μ±ν) > 0, αp+i+1 = (λ + μ + ν + i)/n, αp+n+i+1 = (λ - μ + ν + i)/n, αp+2n+i+1 = (λ + μ - ν + i)/n, αp+3n+i+1 = (λ - μ - ν + i)/n (i = 0, 1, 2, ..., n - 1), βa+i+1 = (2λ + j)/2n (j = 0, 1, 2, ..., 2n - 1).where n is a positive integer, R(λ) > 1⁄2, |arg z| < π, αp+i+1 = (2λ - 1 + i)/2n (i = 0, 1, 2, ..., 2n-1), βq+j+1 = (λ + μ j)/n, βq+n+j+1 = (λ - μ + j)/n (j = 0, 1, 2, ..., n-1).
Rathie, C. B. Integrals involving E-functions. Glasgow mathematical journal, Tome 4 (1960) no. 4, pp. 186-187. doi: 10.1017/S2040618500034134
@article{10_1017_S2040618500034134,
author = {Rathie, C. B.},
title = {Integrals involving {E-functions}},
journal = {Glasgow mathematical journal},
pages = {186--187},
year = {1960},
volume = {4},
number = {4},
doi = {10.1017/S2040618500034134},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034134/}
}
[1] 1.MacRobert, T. M., Functions of a complex variable, 4th edition (1954). Google Scholar
[2] 2.Titchmarsh, E. C., Some integrals involving Bessel functions, J. London Math. Soc. 2 (1927), p. 98. Google Scholar
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