Taiwanese Journal of Mathematics

SOME IDENTITIES CONNECTED WITH A CONTINUED FRACTION OF RAMANUJAN

Bhaskar Srivastava

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Abstract

We first prove two identities which are analogous to Entry 3.3.4 in Ramanujan's lost notebook. The identities in Entry 3.3.4 come out equal to a cubic theta function of Borwein and Borwein [5]. In our case they come out equal to $\frac{(q^4;q^4)^2}{(q^2;q^4)^2} C^2(q)$. We also express $C(q)$ in terms of theta functions $\phi(q)$ and $\psi(q)$. A series expansion of $\log C(q)$ is also given. One of the identities (9) is equivalent to a Theorem in partitions.

Article information

Source
Taiwanese J. Math., Volume 16, Number 3 (2012), 829-838.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406659

Digital Object Identifier
doi:10.11650/twjm/1500406659

Mathematical Reviews number (MathSciNet)
MR2917241

Zentralblatt MATH identifier
1246.33007

Subjects
Primary: 33D15: Basic hypergeometric functions in one variable, $_r\phi_s$

Keywords
basic (or $q$-) series $q$-identities continued fractions $q$-hypergeometric series Rogers-Ramanujan continued fractions

Citation

Srivastava, Bhaskar. SOME IDENTITIES CONNECTED WITH A CONTINUED FRACTION OF RAMANUJAN. Taiwanese J. Math. 16 (2012), no. 3, 829--838. doi:10.11650/twjm/1500406659. https://projecteuclid.org/euclid.twjm/1500406659


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References

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