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Partial second order mock theta functions, their expansions and Pad\'e approximants
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Abstract
By proving a summation formula, we enumerate the expan-sions for the mock theta functions of order 2 in terms of partial mocktheta functions of order 2, 3 and 6. We show a relation between Ramanu-jan's(q)-function and his sixth order mock theta functions. In addition,we also give the continued fraction representation for(q) and 2nd ordermock theta functions and Pade approximants.
참고문헌 (9)
- "Lecture Notes in Math.", (tebook), pp.1018~
- G. A. Baker Jr, "Essentials of Pade approximants" (1975)
- . J. Fine, "With a foreword by George E.Andrews. Mathematical Surveys and Monographs" (1988)
- G. Gasper, "With a foreword by RichardAskey. Encyclopedia of Mathematics and its Applications" (1990), 35. Cambridge UniversityPress
- B. Gordon, "Some eighth order mock theta functions", 62(2), pp.321~335 (2000)
- R. J. McIntosh, "Second order mock theta function" (2004)
- Berlin, "With an introductionby George E. Andrews. Springer-Verlag" (1988), The lost notebook and other unpublished papers Narosa Publishing House
- B. Srivastava, "Ramanujan's mock theta functions", 47, pp.163~174 (2005)
- G. N. Watson, "An account of the mock-theta functions" (1936)
관련 논문AI추천
A comprehensive study of second order mock theta functionsBhaskar Srivastava대한수학회 · 대한수학회보2005 · 제42권 제4호Asymptotic Behaviour of Another Second Order Mock Theta FunctionBhaskar Srivastava경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제3호New indefinite theta series expressions for some even-order mock theta functionsQiuxia Hu, Zeya Jia대한수학회 · 대한수학회보2025 · 제62권 제6호Certain relations for mock theta functions of order eightMaheshwar Pathak, Pankaj Srivastava대한수학회 · 대한수학회논문집2009 · 제24권 제4호Modular Transformations for Ramanujan's Tenth Order Mock Theta FunctionsBhaskar Srivastava경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제2호Explicit evaluations of Ramanujan's remarkable product of theta-functionM. C. Maheshkumar, M. S. M. Naika장전수학회 · Advanced Studies in Contemporary Mathematics2006 · 제13권 제2호
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