If \( y=e^{a \sin ^{-1} x}=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+\ldots \) prove (1) \( \left(1-...

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If \( y=e^{a \sin ^{-1} x}=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}+\ldots \) prove (1) \( \left(1-x^{2}\right) y_{2}=x y_{1}+a^{2} y \)
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