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Collected Papers of Srinivasa Ramanujan

Table of Contents

• Some properties of Bernoulli's numbers
• On Question 330 of Prof. Sanjana
• Note on a set of simultaneous equations
• Irregular numbers
• Squaring the circle
• Modular equations and approximations to $\pi$
• On the integral $\int^x_0\frac{\tan^{-1}t}{t}dt$
• On the number of divisors of a number
• On the sum of the square roots of the first $n$ natural numbers
• On the product $\prod^{n=\infty}_{n=0}[1+(\frac{x}{a+nd})^3]$
• Some definite integrals
• Some definite integrals connected with Gauss's sums
• Summation of a certain series
• New expressions for Riemann's functions $\xi(s)$ and $\Xi(t)$
• Highly composite numbers
• On certain infinite series
• Some formulæ in the analytic theory of numbers
• On certain arithmetical functions
• A series for Euler's constant $\gamma$
• On the expression of a number in the form $ax^2 + by^2 + cz^2 +du^2$
• On certain trigonometrical sums and their applications in the theory of numbers
• Some definite integrals
• Some definite integrals
• A proof of Bertrand's postulate
• Some properties of $p(n)$, the number of partitions of $n$
• Proof of certain identities in combinatory analysis
• A class of definite integrals
• Congruence properties of partitions
• Algebraic relations between certain infinite products
• Congruence properties of partitions
• Une formule asymptotique pour le nombre des partitions de $n$
• Proof that almost all numbers $n$ are composed of about $\log \log n$ prime factors
• Asymptotic formulæ in combinatory analysis
• Asymptotic formulæ for the distribution of integers of various types
• The normal number of prime factors of a number $n$
• Asymptotic formulæ in combinatory analysis
• On the coefficients in the expansions of certain modular functions
• Questions and solutions
• Appendix I: Notes on the papers
• Appendix II: Further extracts from Ramanujan's letters to G. H. Hardy

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