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Generating functions of Legendre polynomials

Generating functions of Legendre polynomials

view  |    137  |  31 Agosto 2011
60 years ago, Fred Brafman derived several \unusual" generating functions of classical orthogonal polynomials,
in particular, of Legendre polynomials Pn(x). His result was a consequence of Bailey's identity for a
special case of Appell's hypergeometric function of the fourth type. In my talk I present a generalisation
of Bailey's identity and its implication to generating functions of Legendre polynomials of the form
¥å
n=0
unPn(x)zn;
where un is an Apery-like sequence, that is, a sequence satisfying
(n+1)2un+1 = (an2+an+b)un 
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