A note on the integral $\smallint ^{\infty }_{0}$ $t^{2\alpha -1}(1+t^{2})$ $^{1-\alpha -\beta }J_{\nu }\ (x\surd (1+t^{2}))dt$
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- by M. L. Glasser PDF
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Abstract:
The integral \[ I_v^{\alpha ,\beta }(x) = \int _0^\infty {{t^{2\alpha - 1}}{{(1 + {t^2})}^{1 - \alpha - \beta }}{J_v}(x} \sqrt {1 + {t^2})} \;dt\] is expressed in terms of Bessel and related functions for various values of the parameters by summing the hypergeometric series representation given by Schmidt.References
- Paul W. Schmidt, Evaluation of the integral $\smallint ^{\infty }_{0}t^{2^{\alpha }-1}J\nu (\chi \surd (1+t^{2}))/(1+t^{2})^{\alpha +\beta -1}dt$, Math. Comp. 32 (1978), no. 141, 265–269. MR 457812, DOI 10.1090/S0025-5718-1978-0457812-4 Y. L. LUKE, The Special Functions and Their Approximations, Academic Press, New York, 1969.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 792-793
- MSC: Primary 33A40
- DOI: https://doi.org/10.1090/S0025-5718-1979-0521293-3
- MathSciNet review: 521293