Abstract
The solution of a number of problems in mathematical physics reduces to finding a function φμ(ν)) from the condition
where P 2p (x) is an associated Legendre function of first kind and ψ μ (x) is a function defined on I ≤ x < ∞ . In other words, the problem reduces to inverting the integral (1) and expanding a given function ψ μ (x) in an integral of associated Legendre functions. The necessity of such transformations arises, for example, in problems related to the use of toroidal and ellipsoidal coordinates.
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Nikolaev, B.G. (1970). The Expansion of an Arbitrary Function in Terms of an Integral of Associated Legendre Functions of First Kind with Complex Index. In: Babich, V.M. (eds) Mathematical Problems in Wave Propagation Theory. Seminars in Mathematics, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0334-4_4
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DOI: https://doi.org/10.1007/978-1-4757-0334-4_4
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