• 호남수학학술지
• /
• 제38권2호
• /
• pp.367-373
• /
• 2016

Adiga and Anitha [1] investigated the Ramanujan's continued fraction (18) to present many interesting identities. Motivated by this work, by using known formulas, we also investigate the Ramanujan's continued fraction (18) to give certain relationships between the Ramanujan's continued fraction and the combinatorial partition identities given by Andrews et al. [3].

• East Asian mathematical journal
• /
• 제32권5호
• /
• pp.609-619
• /
• 2016

Folsom [10] investigated character formulas and Chaudhary [7] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced and investigated combinatorial partition identities. By using and combining known formulas, we aim to present certain interrelationships among character formulas, combinatorial partition identities and continued partition identities.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권1호
• /
• pp.27-42
• /
• 2021

In this paper, we exploit some known theta function identities involving two parameters ��k,n and ��′k,n for the theta function �� to find about 54 new values of the Ramanujan's cubic continued fraction.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.1043-1059
• /
• 2019

In this paper, we use some theta function identities involving two parameters h_n,k and h'_n,k for the theta function φ to establish new evaluations of Ramanujan's cubic continued fraction.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제29권3호
• /
• pp.245-254
• /
• 2022

In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R($e^{-2{\pi}\sqrt{n}}$) and S($e^{-{\pi}\sqrt{n}}$) for $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.

• 호남수학학술지
• /
• 제38권4호
• /
• pp.809-818
• /
• 2016

Chaudhary and Choi [7] presented 14 identities which reveal certain interesting interrelations among character formulas, combinatorial partition identities and continued partition identities. In this sequel, we aim to give slightly modified versions for 8 identities which are chosen among the above-mentioned 14 formulas.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권4호
• /
• pp.377-386
• /
• 2021

In this paper, we use theta-function identities involving parameters 𝑙_5,n, 𝑙'_5,n, and 𝑙'_5,4n to evaluate the Rogers-Ramanujan continued fractions $R(e^{-2{\pi}{\sqrt{n/20}}})$ and $S(e^{-{\pi}{\sqrt{n/5}}})$ for some positive rational numbers n.

• 호남수학학술지
• /
• 제39권2호
• /
• pp.267-273
• /
• 2017

The objective of this note is to establish three results between q-products and combinatorial partition identities in a elementary way. Several closely related q-product identities such as (for example)continued fraction identities and Jacobis triple product identities are also considered.

• East Asian mathematical journal
• /
• 제31권5호
• /
• pp.659-665
• /
• 2015

Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제31권2호
• /
• pp.189-200
• /
• 2024

We derive modular equations of degree 3 to find corresponding theta-function identities. We use them to find some new evaluations of $G(e^{-{\pi}{\sqrt{n}}})$ and $G(-e^{-{\pi}{\sqrt{n}}})$ for $n\,=\,\frac{25}{3{\cdot}4^{m-1}}$ and $\frac{4^{1-m}}{3{\cdot}25}$, where m = 0, 1, 2.