Before&nbsp; the&nbsp; year&nbsp; 1923&nbsp; the&nbsp; literature&nbsp; dealing with generalizedhypergeometric series was somewhat scattered,&nbsp; but&nbsp; in&nbsp; that&nbsp; yearProfessor G.&nbsp; H.&nbsp; Hardy&nbsp; published his&nbsp; paper&nbsp; ''A&nbsp; chapter&nbsp; from&nbsp; Ra-manujan's&nbsp; note-book"&nbsp; in which he gave&nbsp; an&nbsp; account&nbsp; and&nbsp; proofs&nbsp; ofthe&nbsp; results&nbsp; then&nbsp; known,&nbsp; most&nbsp; of&nbsp; which&nbsp; had&nbsp; been rediscovered&nbsp; byRamanujan.&nbsp; Since&nbsp; then&nbsp; numerous papers&nbsp; have&nbsp; been&nbsp; written&nbsp; onthe&nbsp; subject,&nbsp; and&nbsp; it&nbsp; seems desirable&nbsp; that&nbsp; the&nbsp; mass&nbsp; of&nbsp; special results,obtained&nbsp; by&nbsp; one method&nbsp; or&nbsp; another, should be collected together.This is&nbsp; the&nbsp; primary&nbsp; object&nbsp; of&nbsp; this&nbsp; tract.No&nbsp; attempt&nbsp; has been&nbsp; made&nbsp; to&nbsp; give a complete account&nbsp; of&nbsp; theordinary hypergeometric series.&nbsp; In&nbsp; fact&nbsp; the&nbsp; first&nbsp; chapter&nbsp; simplygives&nbsp; the&nbsp; minimum required for&nbsp; the&nbsp; succeeding chapters. Again,all&nbsp; parts&nbsp; of&nbsp; the&nbsp; subject, such as asymptotic expansions, whichdefinitely belong&nbsp; to&nbsp; function theory,&nbsp; have&nbsp; been deliberatelyignored.Although&nbsp; the&nbsp; main&nbsp; part&nbsp; of&nbsp; the&nbsp; work deals&nbsp; with&nbsp; generalizedhypergeometric series,&nbsp; there&nbsp; are also&nbsp; short&nbsp; accounts&nbsp; of&nbsp; Heine'sbasic hypergeometric series&nbsp; and&nbsp; Appell's hypergeometric func-tions&nbsp; of&nbsp; two variables ..My&nbsp; thanks&nbsp; are&nbsp; due&nbsp; to Professor G.&nbsp; H.&nbsp; Hardy&nbsp; who made valuablesuggestions regarding&nbsp; the&nbsp; general plan&nbsp; of&nbsp; the&nbsp; work,&nbsp; and&nbsp; toProfessor L.&nbsp; J.&nbsp; Mordell who suggested&nbsp; the&nbsp; desirability&nbsp; of&nbsp; a&nbsp; tracton this subject.

Generalized Hypergeometric Series PDF

The list of books you might like