Inverse Functions of the Products of Two Bessel Functions.

by William Sollfrey

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A simple, general method of calculating the inverse operator of the product of two spherical (or cylindrical) Bessel functions, as needed for input into an integral expression to determine atmospheric potential from signal phase shift. A method recently published in the Journal of Mathematical Physics (October 1968) uses hypergeometric functions. The technique presented in the present study uses only ordinary algebraic and trigonometric functions when two parameters are integers. If one of them is not an integer, the equation holds if the spherical Bessel functions are replaced by cylindrical Bessel functions. The inverse function vanishes when x equals O, making the calculation of the potential from the phase shift more tractable. 8 pp. Refs. (MW)

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