Generalized prolate spheroidal wave functions
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The following equation
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 n α;β (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.
$$(1 - x^2 )d^2 y/dx^2 + [(\beta - \alpha - (\alpha + \beta + 2)x]dy/dx + (\chi (c) - c^2 x^2 )y = 0$$
KeywordsProlate Inversion Formula Separation Constant Finite Linear Combination Spheroidal Wave Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Indian Academy of Sciences 1977