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INTEGRAL REPRESENTATION OF A FUNCTION IN TERMS OF ASSOCIATED LEGENDRE FUNCTIONS

NANIGOPAL MANDAL and B. N. MANDAL
Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie
Nouvelle Série, Vol. 36 (84), No. 2 (1992), pp. 155-161
Stable URL: http://www.jstor.org/stable/43678461
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
INTEGRAL REPRESENTATION OF A FUNCTION IN TERMS OF ASSOCIATED LEGENDRE FUNCTIONS
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Abstract

An integral representation of a function in terms of associated Legendre functions is developed in this paper. In this integral representation, one variable of integration is with respect to the superscript µ of the associated Legendre function $P_{ - \frac{1} {2} + i\tau }^{ - \mu }$, (cosh α) (0 < α < α₀). This representation may be viewed to generate a Mehler-Fock type integral transform formula fora function f(α) defined in 0 < α < α₀ satisfying certain appropiate conditions.

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