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Let k be an imaginary quadratic eld, h the complex uperhalf plane, and let τ∈h ∩k,q = eπiτ. In this article, we obtain algebraicnumbers from the 130 identities of Rogers-Ramanujan continued fractionsinvestigated in [28] and [29] by using Berndt’s idea ([3]). Using this, weget special transcendental numbers. For example,q1/ 81 +q1+ q +q21+ q2 + ·([1]) is transcendental.
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참고문헌 (10)
참고문헌 신청
/ / On a continued fraction of Ramanujan
/ 19831962191418941981193419521962 / Tata Lectures on Theta I Modular equations and aproximations to π Second memoir on the xpansion of certain innite products Abel’s theo
A / / The rank and the crank in the theory of partitions
Berndt / / Ramanujan’s remarkable product of theta-functions
Duverney / / Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibona ci numbers
/ 19831962191418941981193419521962 / Tata Lectures on Theta I Modular equations and aproximations to π Second memoir on the xpansion of certain innite products Abel’s theo
A / / The rank and the crank in the theory of partitions
Berndt / / Ramanujan’s remarkable product of theta-functions
Duverney / / Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibona ci numbers
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