Hostname: page-component-cb9f654ff-h4f6x Total loading time: 0 Render date: 2025-08-24T08:14:06.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Chapter 2 of Ramanujan's second notebook

Published online by Cambridge University Press:  18 May 2009

Bruce C. Berndt ,
Padmini T. Joshi  and
B. M. Wilson
Bruce C. Berndt
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A.
Padmini T. Joshi
Affiliation:
Department of Mathematics, Ball State University, Muncie, Indiana 47306, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

When Ramanujan died in 1920 he left behind three notebooks containing statements of a few thousand theorems, mostly without proofs. The second notebook is an enlarged edition of the first, and the third is short and fragmentary. Thus our primary attention may be directed toward the second notebook. In the decade following Ramanujan's death, G. N. Watson and B. M. Wilson agreed to perform the enormous task of editing the notebooks. Unfortunately, this task was never completed, possibly, in part, due to the premature death of Wilson in 1935. In 1957, a photostat edition [19] of the notebooks was published, but no editing whatsoever was undertaken.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 2 , July 1981 , pp. 199 - 216
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Aitken, A. C., On Bernoulli's numerical solution of algebaic equations, Proc. Roy. Soc. Edinburgh, Sect. A 46 (1926), 289–305.CrossRefGoogle Scholar
2.Ayoub, R., An introduction to the analytic theory of numbers, (American Mathematical Society, Providence, 1963).Google Scholar
3.Berndt, B. C., Ramanujan's notebooks, Math. Mag. 51 (1978), 147–164.CrossRefGoogle Scholar
4.Berndt, B. C., Chapter 14 of Ramanujan's second notebook, Enseignement Math. 26 (1980), 1–65.Google Scholar
5.Bromwich, T. J. I'a., An introduction to the theory of infinite series, second ed., (Macmillan, London, 1926).Google Scholar
6.Chrystal, G., Algebra, Part II, second ed., (A. and C. Black, London, 1922).Google Scholar
7.Glaisher, J. W. L., A theorem in trigonometry, Quart. J. Math. Oxford 15 (1878), 151–157.Google Scholar
8.Glasser, M. L. and Klamkin, M. S., On some inverse tangent summations, Fibonacci Quart. 14 (1976), 385–388.Google Scholar
9.Hadamard, J. S. et Mandelbrojt, M., La Serie de Taylor, (Gauthier-Villars, Paris, 1926).Google Scholar
10.Hansen, E. R., A table of series and products, (Prentice-Hall, Englewood Cliffs, 1975).Google Scholar
11.Henrichi, P., Applied and computational complex analysis, Vol. 1, (John Wiley & Sons, New York, 1974).Google Scholar
12.Lionnet, M., Question 1294, solution by M. A. Laisant, Nouv. Ann. Math., Ser. 2, 18 (1879), 330–332.Google Scholar
13.Loney, S. L., Plane trigonometry, Part II, (University Press, Cambridge, 1952).Google Scholar
14.Ramanujan, S., On the integral , J. Indian Math. Soc. 7 (1915), 93–96.Google Scholar
5.Ramanujan, S., On the product a, J- Indian Math. Soc. 7 (1915), 209–211.Google Scholar
16.Ramanujan, S., Question 260, J. Indian Math. Soc. 3 (1911), 43.Google Scholar
17.Ramanujan, S., Question 261, J. Indian Math. Soc. 3 (1911), 43.Google Scholar
18.Ramanujan, S., Collected papers, (Chelsea, New York, 1962).Google Scholar
19.Ramanujan, S., Notebooks (2 volumes), (Tata Institute of Fundamental Research, Bombay, 1957).Google Scholar
20.Titchmarsh, E. C., The theory of functions, second ed., (Oxford University Press, London, 1939).Google Scholar
21.Wheelon, A. D., Tables of summable series and integrals involving Bessel functions, (Holden-Day, San Francisco, 1968).Google Scholar
22.Whittaker, E. T. and Robinson, G., The calculus of observations, second ed., (Blackie and Son, Glasgow, 1926).Google Scholar
23.Wright, E. M., Solution of the equation ze z = a, Bull. Amer. Math. Soc. 65 (1959), 89–93.CrossRefGoogle Scholar
24.Wright, E. M., Solution of the equation ze z = a, Proc. Roy. Soc. Edinburgh, Sect. A 65 (1959), 192–203.Google Scholar
25.Wright, E. M., Solution of the equation (pz + q)e z = rz + s, Bull. Amer. Math. Soc. 66 (1960), 277–281.CrossRefGoogle Scholar
26.Wright, E. M., Solution of the equation (z + b)ez + a = ±(z + b), Proc. Roy. Soc. Edinburgh, Sect. A 65 (1960/1961), 358–371.Google Scholar
27.Wright, E. M., Stability criteria and the real roots of a transcendental equation, SIAM J. Appl. Math. 9 (1961), 136–148.CrossRefGoogle Scholar