Formula:KLS:09.09:11

<< Formula:KLS:09.09:10

formula in Pseudo Jacobi

Formula:KLS:09.09:12 >>

${\displaystyle{\displaystyle{\displaystyle\frac{d}{dx}\left[(1+x^{2})^{-N-1}{\mathrm{e}^{2\nu\operatorname{arctan}x}}P_{n}\!\left(x;\nu,N\right)\right]{}=(n-2N-2)(1+x^{2})^{-N-2}{\mathrm{e}^{2\nu\operatorname{arctan}x}}P_{n+1}\!\left(x;\nu,N+1\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\mathrm{e}}}}$ : the base of the natural logarithm : http://dlmf.nist.gov/4.2.E11
${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : pseudo Jacobi polynomomal : http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi

Bibliography

Equation in Section 9.9 of KLS.

URL links

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<< Formula:KLS:09.09:10

formula in Pseudo Jacobi

Formula:KLS:09.09:12 >>