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An infinite integral formula

Published online by Cambridge University Press:  20 January 2009

C. G. Lambe
C. G. Lambe
Affiliation:
Royal Military Academy, Woolwich, S.E.18.
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§ 1. The object of this note is to discuss the formula

the integral being supposed convergent for certain ranges of values of x and z. The contour is such that the poles of Γ(– s)lie to its right and the other poles of the integrand to its left. It will be seen that all the Pincherle-Mellin-Barnes integrals are particular cases of this formula.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 6 , Issue 2 , October 1939 , pp. 75 - 77
Copyright
Copyright © Edinburgh Mathematical Society 1939

References

page 75 note 1 Proc. Boy. Soc., Edin , 48 (1927–1928), 92.Google Scholar

page 76 note 1 Proc. Edin. Math. Soc. (2), 3 (1931), 189.Google Scholar

page 76 note 2 CfWhittaker, and Watson, , Modem Analysis (Cambridge, 1927), §14·5.Google Scholar