Asymptotic Formulaae in Combinatory Analysis

1918/01/01 by G. H. Hardy, S. Ramanujan · 39 citations
Mathematics · #Advanced Mathematical Identities #Advanced Combinatorial Mathematics #Analytic Number Theory Research

paper · doi:10.1112/plms/s2-17.1.75

Abstract

This term vanishes identically.«* Both F a (z) and x« (*) are two-valued in D. The value of F,, (x) contemplated is naturally that represented by the power series.* Here, and in many passages in our subsequent argument, it is to be remembered that the number of values of p, corresponding to a given q, is less than q, and that the number of values of q is of order Sn.Thus we have generally * Cf.MucMahon, loc.cit., p. 11.We give at the end of the paper a table (Table V) of the values of q (n) up to n = 100.This table was calculated by Mr.

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