Description 
1 online resource (xvii, 439 pages) : illustrations 
Contents 
88001 1. Introduction  2. Double series of Bessel functions and the circle and divisor problems  3. Koshliakov's formula and Guinand's formula  4. Theorems featuring the gamma function  5. Hypergeometric series  6. Two partial manuscripts on Euler's constant y  7. Problems in diophantine approximation  8. Number theory  9. Divisor sums  10. Identities related to the Riemann zeta function and periodic zeta functions  11. Two partial unpublished manuscripts on sums involving primes  12. An unpublished manuscript of Ramanujan on infinite series identities  13. A partial manuscript on Fourier and Laplace transforms  14. Integral analogues of theta functions and Gauss sums  15. Functional equations for products of Mellin transforms  16. A preliminary version of Ramanujan's paper "On the product [mathematical equation]"  17. A preliminary version of Ramanujan's paper "On the integral [mathematical equation]"  18. A partial manuscript connected with Ramanujan's paper "Some definite integrals"  19. Miscellaneous results in analysis  20. Elementary results  21. A strange, enigmatic partial manuscript 

88001/(S Introduction  Double Series of Bessel Functions and the Circle and Divisor Problems  Koshliakov's Formula and Guinand's Formula  Theorems Featuring the Gamma Function  Hypergeometric Series  Two Partial Manuscripts on Euler's Constant γ  Problems in Diophantine Approximation  Number Theory  Divisor Sums  Identities Related to the Riemann Zeta Function and Periodic Zeta Functions  Two Partial Unpublished Manuscripts on Sums Involving Primes  An Unpublished Manuscript of Ramanujan on Infinite Series Identities  A Partial Manuscript on Fourier and Laplace Transforms  Integral Analogues of Theta Functions and Gauss Sums  Functional Equations for Products of Mellin Transforms  A Preliminary Version of Ramanujan's Paper "On the Product πn=0[infinity][1+(xa+nd)3] "  A Preliminary Version of Ramanujan's Paper "On the Integral [integral]x0tan1ttdt "  A Partial Manuscript Connected with Ramanujan's Paper "Some Definite Integrals"  Miscellaneous Results in Analysis  Elementary Results  A Strange, Enigmatic Partial Manuscript 
Summary 
"In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the fourth of five volumes that the authors plan to write on Ramanujan's lost notebook. In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on qseries. Most of the entries examined in this volume fall under the purviews of number theory and classical analysis. Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems."Publisher's description 
Analysis 
Global analysis (Mathematics) 

Fourier analysis 

Functions, special 

Number theory 

Analysis 

Special Functions 
Bibliography 
Includes bibliographical references (pages 421434) and index 
Notes 
English 

Online resource; title from PDF title page (SpringerLink, viewed November 7, 2013) 
Subject 
Ramanujan Aiyangar, Srinivasa, 18871920.


Ramanujan Aiyangar, Srinivasa, 18871920 

Mathematical analysis.


Number theory.


Mathematicians  India  Biography


Mathematics.


Mathematics


BIOGRAPHY & AUTOBIOGRAPHY  Science & Technology.


MATHEMATICS  Essays.


MATHEMATICS  PreCalculus.


MATHEMATICS  Reference.


Análisis matemático


Matemáticos  Biografías  India


Matemáticas


Números , Teoría de


Mathematics


Mathematical analysis


Mathematicians


Number theory


India 

India

Genre/Form 
Biographies


Biographies.


Biographies.

Form 
Electronic book

Author 
Berndt, Bruce C., 1939

ISBN 
9781461440819 

1461440815 

1461440807 

9781461440802 

1322332711 

9781322332710 
