Difference between revisions of "User:Tohline/Math/EQ Toroidal05"
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(Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templat…') |
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[https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erdélyi (1953)]: Volume I, §3.12, p. 169, eq. ( | [https://authors.library.caltech.edu/43491/1/Volume%201.pdf A. Erdélyi (1953)]: Volume I, §3.12, p. 169, eq. (1) | ||
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Latest revision as of 21:39, 1 July 2018
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<math>~ \int_a^b\biggl[(\nu - \sigma)(\nu + \sigma + 1) + (\rho^2 - \mu^2)(1 - z^2)^{-1} \biggr] w_\nu^\mu ~w_\sigma^\rho ~dz </math> |
<math>~=</math> |
<math>~ \biggl[ z(\nu-\sigma) w_\nu^\mu ~w_\sigma^\rho + (\sigma+\rho) w_\nu^\mu ~ w_{\sigma-1}^\rho - (\nu + \mu) w_{\nu - 1}^\mu ~w_\sigma^\rho \biggr]_a^b </math> |
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A. Erdélyi (1953): Volume I, §3.12, p. 169, eq. (1) |
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| where, <math>~w_\nu^\mu(z)</math> and <math>~w_\sigma^\rho(z)</math> denote any solutions of Legendre's differential equation |