Probabilistic derivation of a bilinear summation formula for the Meixner-Pollaczek polynominals
1980 ◽
Vol 3
(4)
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pp. 761-771
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Keyword(s):
Using the technique of canonical expansion in probability theory, a bilinear summation formula is derived for the special case of the Meixner-Pollaczek polynomials{λn(k)(x)}which are defined by the generating function∑n=0∞λn(k)(x)zn/n!=(1+z)12(x−k)/(1−z)12(x+k), |z|<1.These polynomials satisfy the orthogonality condition∫−∞∞pk(x)λm(k)(ix)λn(k)(ix)dx=(−1)nn!(k)nδm,n, i=−1with respect to the weight functionp1(x)=sech πxpk(x)=∫−∞∞…∫−∞∞sech πx1sech πx2 … sech π(x−x1−…−xk−1)dx1dx2…dxk−1, k=2,3,…
2021 ◽
Vol 0
(0)
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pp. 0
Keyword(s):
2010 ◽
Vol DMTCS Proceedings vol. AN,...
(Proceedings)
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Keyword(s):
2021 ◽
Vol 4
(2)
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pp. 52-65
2014 ◽
Vol DMTCS Proceedings vol. AT,...
(Proceedings)
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2012 ◽
Vol 01
(04)
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pp. 1250010
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