Ramanujan’s Notebooks

1. Front Matter

   Pages I-X

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2. Introduction

   • Bruce C. Berndt

   Pages 1-15

3. Magic Squares

   • Bruce C. Berndt

   Pages 16-24

4. Sums Related to the Harmonic Series or the Inverse Tangent Function

   • Bruce C. Berndt

   Pages 25-43

5. Combinatorial Analysis and Series Inversions

   • Bruce C. Berndt

   Pages 44-84

6. Iterates of the Exponential Function and an Ingenious Formal Technique

   • Bruce C. Berndt

   Pages 85-108

7. Eulerian Polynomials and Numbers, Bernoulli Numbers, and the Riemann Zeta-Function

   • Bruce C. Berndt

   Pages 109-132

8. Ramanujan’s Theory of Divergent Series

   • Bruce C. Berndt

   Pages 133-149

9. Sums of Powers, Bernoulli Numbers, and the Gamma Function

   • Bruce C. Berndt

   Pages 150-180

10. Analogues of the Gamma Function

    • Bruce C. Berndt

    Pages 181-231

11. Infinite Series Identities, Transformations, and Evaluations

    • Bruce C. Berndt

    Pages 232-294

12. Back Matter

    Pages 295-357

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Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education inmathematics, he taught himself, and managed to produce many important new results. With the support of the English number theorist G. H. Hardy, Ramanujan received a scholarship to go to England and study mathematics. He died very young, at the age of 32, leaving behind three notebooks containing almost 3000 theorems, virtually all without proof. G. H. Hardy and others strongly urged that notebooks be edited and published, and the result is this series of books. This volume dealswith Chapters 1-9 of Book II; each theorem is either proved, or a reference to a proof is given.

• calculus
• exponential function
• transformation

• Department of Mathematics, University of Illinois, Urbana, USA

  Bruce C. Berndt

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