Titlebook: Ramanujan‘s Lost Notebook; Part II George E. Andrews,Bruce C. Berndt Book 2009 Springer-Verlag New York 2009 Invariant.approximation.ellipt

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搏斗

The Heine Transformation,E. Heine [178], [179, pp. 97–125] was the first to generalize Gauss’s hypergeometric series to .-hypergeometric series by defining, for ., ., where . and where, for each nonnegative integer ., ..

Anecdote

摻和

初次登臺(tái)

Well-Poised Series,Among Ramanujan’s most far-reaching and striking discoveries are the Rogers–Ramanujan identities, given for . by [241], [31, Chapter 10] . and . In the lost notebook, we find many identities of the Rogers–Ramanujan type; see, for example, Chapter 11 of our first book [31].

Protein

,Bailey’s Lemma and Theta Expansions,Most of the entries to be established in this chapter were originally proved in [22]. That paper appeared before the discoveries presented in [24] were made. It is now possible to present these results in a way that makes clear their relationship to the hierarchy of .-hypergeometric identities growing out of Bailey’s lemma [41, equation (3.1)].

Folklore

自負(fù)的人

Two Letters on Eisenstein Series Written from Matlock House,As we mentioned in Chapter 11, in their last joint paper, G.H. Hardy and Ramanujan [177], [242, pp. 310–321] established the following remarkable formula for the coefficients of 1/...Then,

Trigger-Point