This paper gives a short but reasonably comprehensive review of Ramanujan's {_1\\psi_1} summation and its generalisations. It covers the history of Ramanujan's summation, simple applications to sums of squares and orthogonal polynomials, non-commutative generalisations, and generalisations to ...
2. History The first integral theorem in the spirit of Ramanujan's Master Theorem appears to have been given by Glaisher in 1874, [10]: (2.1) ∞ 0 a0 − a1x2 + a2x4 − . . . π dx = 2 a− 1 2 . Glaisher writes, "of course, an being only defined for n a positive ...
It covers the history of Ramanuj... SO Warnaar - 《Electronic Transactions on Numerical Analysis》 被引量: 1发表: 2012年 Ramanujan's $_{1}\\\psi_{1}$ summation theorem —perspective, announcement of bilateral $q$-Dixon–Anderson and $q$-Selberg integral extensions, and conte... The Ramanu...
His MONTHLY article "The Curious History of Fa谩 di Bruno's Formula" (March, 2002) was honored with a 2003 Lester R. Ford Award. He has never used the phrase mutatis mutandis before, but it is one of Askey's favorites. He is interested in eighteenth and nineteenth century analysis, ...
1 The collection [1] contains both original papers of Vieta and Wallis as well as other fundamental papers in the history of π. Indeed, there are many good historical sources on π. The text by P. Eymard and J. P. Lafon [6] is an excellent place to start. Wallis's formula (1.1)...
摘 要 式,再利用Sears.变换推导出若干Rogers.Ramanujan型恒等式. 然后利用关于q一微分算子的Leibniz公式给出了一些重要变换公式新的证明,包 括q-Z项式定理,q.Chu.Vandermonde和. 定理,Sears.变换,Leibniz.法则 ABSTRACT The of hasbeenmorethantWO iden— historyq-series hundred,Rogers—Ramanujantype tities acen...
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