An entry of Ramanujan on hypergeometric series in his Notebooks |
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| Affiliation: | 1. Flemish Academic Center (VLAC), Royal Flemish Academy of Belgium for Science and the Arts, Paleis der Academiën, Hertogsstraat 1, Brussels B-1000, Belgium;2. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India;3. Universiteit Gent, Toegepaste Wiskunde en Informatica, Krijgslaan 281-S9, Gent B-9000, Belgium;4. Institut Girard Desargues, Université Claude Bernard Lyon-I, 21, avenue Claude Bernard, Villeurbanne F-69622, Cedex, France |
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| Abstract: | Example 7, after Entry 43, in Chapter XII of the first Notebook of Srinivasa Ramanujan is proved and, more generally, a summation theorem for 3F2(a,a,x;1+a,1+a+N;1), where N is a nonnegative integer, is derived. |
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| Keywords: | Hypergeometric functions Gamma function Digamma function Ramanujan's Notebooks Summation theorems |
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