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Multiple integrals involving product of modified Bessel functions of the second kind

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Abstract

The following two multiple integrals are evaluated

$$\prod\limits_{r = 1}^{m - 1} {\int\limits_0^\infty {\lambda _r^{k_r } K_{\gamma r} (\lambda _r )d\lambda _r K_\mu } \left[ {x\left( {\lambda _1 ...\lambda _{m - 1} } \right)^{ \pm 1} } \right].} $$

Also the asymptotic behavior of the two integrals as |x|→0 and as |x|→∞ is given.

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References

  1. Mac Robert T. M.,Functions of a complex variable, 5th edit. 1962.

  2. Erdelyi A., Magnus W., Oberhetinger F. and Tricomi E.,Higher transcendental functions, Vol. 1, Mc Graw Hill, 1953.

  3. Titchmarch E. C.,Introduction to the theory of Fourier Integrals, Oxford, 1937.

  4. Mac Robert T. M.,Multiplication formulae for the E-functions regarded as functions of their parameters, Pacific Journal of Math., Vol. 9 (1959).

  5. Hardy G. H., Messen. of Math., 56, 1927.

  6. Titchmarch E. C.,Some integrals involving Bessel-functions, Journ. London Math. Soc., (2) (1927).

  7. Barnes E. W.,The asymptotic expansion of integral functions defined by Taylor series, Phil. Trans. Roy. Soc. London A. Vol. 206, 1906.

  8. Barnes E. W.,The asymptotic expansions of integral functions defined by generalized hypergeometric functions, Proc. Lond. Math. Soc. (2), 1907.

  9. Wright E. M.,The asymptotic expansion of the generalized hypergeometric functions, J. Lond. Math. Soc., 10, 1955.

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Authors and Affiliations

  1. Madison, U. S. A.

    F. M. Ragab

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  1. F. M. Ragab
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Additional information

Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-11-022-ORD-2059.

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Ragab, F.M. Multiple integrals involving product of modified Bessel functions of the second kind. Rend. Circ. Mat. Palermo 14, 367–381 (1965). https://doi.org/10.1007/BF02844037

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  • DOI: https://doi.org/10.1007/BF02844037

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