Abstract
We consider the integral\(\int\limits_0^\infty {xe^{ - \eta x^2 } } J_b (Kx)Y_b (kx)dx\) whereη, K, k andb are all positive real numbers. We reduce this integral to a linear combination of two integrals. The first of these is an exponential integral, which can be expressed as a difference of two Shkarofsky functions, or can easily be evaluated numerically. The second is the original integral, but withk andK both replaced by √kK. We express this as a MeijerG function, and then reduce it to the sum of an associated Bessel function and a modified Bessel function.
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Previously at the Maple Symbolic Computation Group, University of Waterloo, Waterloo, Ontario, Canada, N2L-3G1
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McPhedran, R.C., Dawes, D.H. & Scott, T.C. On a bessel function integral. AAECC 2, 207–216 (1992). https://doi.org/10.1007/BF01294334
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DOI: https://doi.org/10.1007/BF01294334