Integrals Involving a Modified Bessel Function of the Second Kind and an E-Function
- 1 October 1954
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association
- Vol. 2 (2) , 93-96
- https://doi.org/10.1017/s2040618500033098
Abstract
The first formula to be proved iswhere p ≧ q + 1, | amp z | < л, R(k±n + αr)>0, r = l, 2, …, p. For other values of p and q the result is valid if the integral is convergent. A second formula is given in § 3.The following formulae are required in the proof:where R(z);>0, (1);where R(α)>0, | amp z | < л, (2);where the contour starts from -∞ on the ξ-axis, passes round the origin in the positive direction, and ends at -∞ on the ξ-axis, the initial value of amp ζ being - л, (3).This publication has 2 references indexed in Scilit:
- An Integral Involving a Product of Two Modified Bessel Functions of the Second KindProceedings of the Glasgow Mathematical Association, 1954
- An Infinite Integral involving a Product of Two Modified Bessel Functions of the Second KindProceedings of the Glasgow Mathematical Association, 1953