express the function z in terms of Legendre functions

Question:express the function z in terms of Legendre functions

Posted: fatemeh1090 65 Product: Maple 2019

August 31 2020

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

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