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Integrals Involving a Modified Bessel Function of the Second Kind and an E-Function
Published online by Cambridge University Press: 18 May 2009
Extract
The first formula to be proved is
where 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).
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- Copyright © Glasgow Mathematical Journal Trust 1954
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