Probability distribution and a self-reciprocal relation involving confluent hypergeometric functions

✍ Scribed by P.A. Lee

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 238 KB
• Volume: 334
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(96)00073-7

✦ Synopsis

The mixture model formulation of the non-central negative binomial distribution e"~q'+'L~'(-~q)~~hereR>O,v>-l,O<p=1-q<1,andk=0,1,2,...isusedtoprovide a probabilistic proof of the following self-reciprocal relation involving conjuent hypergeometric functions under Hankel trawform of order v:

s ~'(xy)"iJ,,(xy)x.i"2e~~2'2 ,F,(-n;l+v/2-n/2;x2/2)dx = (_ l)nyV+lr2e-~'/2 ,F ,(-nn;l+v/2-n/2;y2/2).