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

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9.17 Representing the solutions to certain second-order differential equations using a Riemann scheme

9.171 The hypergeometric equation (see 9.151):

u=P{ 010α01γβγαβz }

si140_e  WH

9.172 The associated Legendre's equation defining the functions pnm(z)si0070_e for n and m integers (see 8.7001):

1. 

u=P{ 0112mn+112m1z212mn12m }

si141_e  WH

2. 

u=P{ 0112n12m011z2n+1212m12 }

  WH

9.173 The function pnm(1z22n2) satisfies the equation

u=P{ 4n2012mn+112

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