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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

A note on the integral $ \smallint \sp{\infty }\sb{0}$ $ t\sp{2\alpha -1}(1+t\sp{2})$ $ \sp{1-\alpha -\beta }J\sb{\nu }\ (x\surd (1+t\sp{2}))dt$


Author: M. L. Glasser
Journal: Math. Comp. 33 (1979), 792-793
MSC: Primary 33A40
MathSciNet review: 521293
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Abstract: The integral

$\displaystyle I_v^{\alpha ,\beta }(x) = \int_0^\infty {{t^{2\alpha - 1}}{{(1 + {t^2})}^{1 - \alpha - \beta }}{J_v}(x} \sqrt {1 + {t^2})} \;dt$

is expressed in terms of Bessel and related functions for various values of the parameters by summing the hypergeometric series representation given by Schmidt.

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DOI: https://doi.org/10.1090/S0025-5718-1979-0521293-3
Article copyright: © Copyright 1979 American Mathematical Society