✦ LIBER ✦

On A Result of Ramanujan on Theta Functions

✍ Scribed by S.S. Rangachari

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 261 KB
Volume: 48
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1072

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On the Logarithmic Derivative of a Theta

On the Logarithmic Derivative of a Theta Function and a Fundamental Identity of Ramanujan

✍ L.C. Shen 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 216 KB

On the Circular Summation of the Elevent

On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function

✍ Ken Ono 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 94 KB

Let f (a, b) denote Ramanujan's theta series. In his ``Lost Notebook'', Ramanujan claimed that the ``circular'' summation of n th powers of f satisfies a factorization of the form f (a n , b n ) F n (a n b n ) where F n (q)=1+2nq (n&1)Â2 + } } } . Moreover, he listed explicit closed formulas for F 2

On some applications of Jacobi's theta-f

On some applications of Jacobi's theta-functions

✍ R. T. A. Innes 📂 Article 📅 1909 🏛 John Wiley and Sons 🌐 English ⚖ 70 KB 👁 2 views

On Ramanujan's Quartic Theory of Ellipti

On Ramanujan's Quartic Theory of Elliptic Functions

✍ Bruce C. Berndt; Heng Huat Chan; Wen-Chin Liaw 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 174 KB

In his famous paper [11], [12, pp. 23 39], Ramanujan offers several elegant series for 1Â?. He then remarks, ``There are corresponding theories in which q is replaced by one or other of the functions'' where r=3, 4, or 6 and where 2 F 1 denotes the classical Gaussian hypergeometric function. In the

A New Class of Theta-Function Identities

A New Class of Theta-Function Identities Originating in Ramanujan′s Notebooks

✍ B.C. Berndt; L.C. Zhang 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 447 KB

In the unorganized pages of his second notebook, Ramanujan offers two new theta-function identities that have a form different from other identities found in the literature. Using the theory of modular forms, we prove a general theorem containing Ramanujan's two identities as special cases. 1994 Aca

On Certain Identities Of Ramanujan

✍ Zhi-Guo Liu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 127 KB

In this paper we will start with one identity of Ramanujan about Lambert series related to modular relations of degree 7 to give some completely new proofs of several important theta functions identities proved by Berndt and Zhang [1994, J. Number Theory 48, 224 242] via the theory of modular forms.