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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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7.21 Integration of associated Legendre functions with respect to the order

7.211

1. 

0Px12(cosθ)dx=12cosec(12θ)[0<θ<π]

si295_e  ET II 329(19)

2. 

Px(cosθ)dx=cosec(12θ)[0<θ<π]

si296_e  ET II 329(20)

7.212

0x1tanh(πx)P12+ix(cosha)dx=2e12aK(ea)

si297_e  ET II 330(22)

[a > 0]

7.213

0xtanh(πx)a2+x2P12+ix(coshb)dx=Qa12(coshb)[Rea>0]

si298_e  ET II 387(23)

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