An Expansion of the Gegenbauer Polynomial (Cn superscript mu)(xy).
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An expansion of the Gegenbauer polynomial Cn superscript muxy in an orthogonal series in the polynomials Ck superscript lambdax with coefficients depending on y is derived. The coefficients of Ck superscript lambdax in the expansion are derived in a form that, by inspection, shows them to be positive for y 1 and mu or lambda or 0. A limiting form for these expansion coefficients is also derived. This limiting form, together with an apparently new formula of Mehler-Heine type, is shown to imply Sonines second finite integral. Author
- Numerical Mathematics