On certain expansions involving Whittaker's \(M\)-functions. (Q2586656)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On certain expansions involving Whittaker's \(M\)-functions. |
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On certain expansions involving Whittaker's \(M\)-functions. (English)
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1940
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\[ \begin{aligned} &x^{-\frac{1}{2}}M_{k,-m}^2(x) = \sum\limits_{r=0}^\infty A_rM_{2k+2r+\frac{1}{2},-2m}(2x), \\ &x^{-\frac{1}{2}}M_{k,-m}^2(x) = \sum\limits_{r=0}^\infty B_rM_{\frac{1}{2}-2k+2r,-2m}(2x). \end{aligned} \] Dabei sind die \(A_r\), \(B_r\) durch die Differentialgleichung für die \(M_{k,-m}^2(x)\) bestimmt.
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