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Generalized prolate spheroidal wave functions

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Abstract

The following equation

$$(1 - x^2 )d^2 y/dx^2 + [(\beta - \alpha - (\alpha + \beta + 2)x]dy/dx + (\chi (c) - c^2 x^2 )y = 0$$

has been solved wherex(c) a separation constant is the characteristic value and is a function ofc. This solution is a generalization of spheroidal wave function into the series form ofP α;β n (x),α andβ both separately are greater than −1. The finite transform and its properties have been defined and a boundary value problem has been solved applying these tools.

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References

  1. Flammer, C.,Spheroidal Wave Functions (Stanford Univ. Press, Stanford) (1957).

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Authors and Affiliations

  1. Department of Mathematics, M.R. Engineering College, Jaipur

    R. K. Gupta

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  1. R. K. Gupta
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Gupta, R.K. Generalized prolate spheroidal wave functions. Proc. Indian Acad. Sci. 85, 104–114 (1977). https://doi.org/10.1007/BF03046817

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  • DOI: https://doi.org/10.1007/BF03046817

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