HYPERGEOMETRIC FORMS OF SOME FUNCTIONS INVOLVING ARCSINE (x) USING DIFFERENTIAL EQUATION APPROACH
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 |
Abstract
In this paper, by changing the independent and dependent variables in the suitable ordinary differential equations of second and third order and comparing the resulting ordinary differential equations with standard ordinary hypergeometric differential equations of Gauss and Clausen, we obtain the hypergeometric forms of following functions:
\begin{equation*}
\frac{\sin^{-1}(x)}{\sqrt{(1-x^2)}},~~~[{\sin^{-1}(x)}]^{2}~~~and~~~{\sin^{-1}(x)}.
\end{equation*}
Keywords and Phrases
Hypergeometric functions, Ordinary differential equations.
A.M.S. subject classification
33C20, 34-XX
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