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

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8.75 Special cases and particular values

8.751

1. 

Pνm(x)=(1)mΓ(ν+m+1)(1x2)m22mΓ(νm+1)m!F(mν,m+ν+1;m+1;1x2)

si1370_e  MO 84

2. 

Pνm(z)=Γ(ν+m+1)(z21)m22mm!Γ(νm+1)F(mν,m+ν+1;m+1;1z2)

si1371_e  MO 84

3.8 

Qn+12μ(z)=eμπiΓ(μ+n+32)2n+32(n+1)!(z21)μ2π1/2znμ3/2F(μ+n+522,μ+n+322;n+2;1z2)

si1372_e  MO 84

8.752

1. 

Pνm(x)=(1)m(1x2)m2dmdxmPν(x)

si1373_e  WH, MO 84, EH I ...

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