Generalized Watson's summation formula for 3F2(1)

✍ Scribed by Stanisław Lewanowicz

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 415 KB
• Volume: 86
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(97)00170-2

✦ Synopsis

A summation formula is given for 3Fz(a,b,c; ½(a + b +i+ 1),2c +j; 1) with fixed j and arbitrary i (i, jE71). This result generalizes the classical Watson's theorem which deals with the case i =j = 0.

Extensions to the cases of 3F2(a, 1 + i + j -a, c; e, 1 + i + 2c -e; 1 ), and 3Fz(a, b, c; 1 + i + a -b, 1 + i + j + a -c; 1) are given. Notice that the case i =j = 0 corresponds to the classical theorems due to Whipple and Dixon, respectively.