A Logarithmic Derivative of Theta Function and Implication
Pure and Applied Mathematics Journal
Volume 4, Issue 5-1, October 2015, Pages: 55-59
Received: Jun. 26, 2015;
Accepted: Jun. 28, 2015;
Published: Jun. 30, 2016
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Yaling Men, School of Mathematics, Xianyang Vocational and Technical College, Xianyang, P. R. China
Jiaolian Zhao, School of Mathematics and Informatics, Weinan Teacher`s University, Weinan, P. R. China
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In this paper we establish an identity involving logarithmic derivative of theta function by the theory of elliptic functions. Using these identities we introduce Ramanujan’s modular identities, and also re-derive the product identity, and many other new interesting identities.
Theta Function, Elliptic Function, Logarithmic Derivative
To cite this article
A Logarithmic Derivative of Theta Function and Implication, Pure and Applied Mathematics Journal. Special Issue: Mathematical Aspects of Engineering Disciplines.
Vol. 4, No. 5-1,
2015, pp. 55-59.
W. N .Bailey, A further note on two of Ramanujan’s formulae, Q. J. Math.(Oxford) 3 (1952), pp.158-160.
R. Bellman, A brief introduction to the theta functions, Holt Rinehart and Winston, New York(1961).
B. C. Berndt, Ramanujan’s Notebooks III, Springer-Verlag, New York (1991).
J.M. Borwein and P. B. Borwein, Pi and the AGM- A Study in Analytic Number Theory and Computational Complexity, Wiley, N.Y., 1987.
J.M. Borwein, P. B. Borwein and F. G. Garvan, Some cubic modular Indentities of Ramanujan, Trans. of the Amer. Math. Soci., Vol. 343, No. 1 (May, 1994), pp.35-47
J. A. Ewell, On the enumerator for sums of three squares, Fibon.Quart.24(1986), pp.151-153.
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. Cambridge Univ. Press, 1966
Li-Chien Shen, On the Additive Formulae of the Theta Functions and a Collection of Lambert Series Pertaining to the Modular Equations of Degree 5, Trans. of the Amer. Math. Soci. Vol. 345, No. 1 (Sep., 1994), pp.323-345.