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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 no.2 Bogotá July/Dec. 2019 Epub Mar 20, 2020
Artículos originales
Generalized Bilateral Eighth Order Mock Theta Functions and Continued Fractions
Funciones Theta Mock generalizadas en dos variables de orden ocho
1University of Lucknow, Lucknow, India, Department of Mathematics and Astronomy University of Lucknow, Lucknow, India e-mail: bhaskarsrivastav@yahoo.com
We give a two independent variable generalization of bilateral eighth order mock theta functions and expressed them as infinite product. On specializing parameters, we have given a continued fraction representation for the generalized function, which I think is a new representation.
Keywords and phrases. q-Hypergeometric series; Mock theta functions; Continued fraction
En esta contribución se obtienen funciones Theta Mock generalizadas de orden ocho en dos variables que se expresan mediante un producto infinito. Para valores particulares de los parámetros se deducen representaciones de dichas funciones mediante fracciones continuas.
Palabras y frases clave. funciones Theta Mock; fraccioón continuada; orden ocho en dos variables
Acknowledgments.
I am thankful to the Referee for his valuable comments and suggestions.
References
[1] G. Gasper and M. Rahman, Basic Hypergeometric Series, Encycl. Math. Applics., Vol. 35, Cambridge University Press, Cambridge, 1990. [ Links ]
[2] B. Gordon and R.J. McIntosh, Some eighth order mock theta functions, J. London Math. Soc. 62(2) (2000), 321-335. [ Links ]
[3] J. Mc Laughlin, Mock Theta Function Identities Deriving from Bilateral Basic Hypergeometric Series, Analytic Number Theory, Modular Forms and q-Hypergeometric Series, Springer Proc. Math. Stat., Springer, Cham. 221 (2017), 503-531. [ Links ]
[4] S. Ramanujan, Collected Papers, Cambridge University Press, Cambridge , 1927; reprinted by Chelsea, New York 1962 ; reprinted by the American Mathematical Society, Providence, RI, 2000. [ Links ]
[5] L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. 54 (1952), 147-167. [ Links ]
Received: 2019; Accepted: August 2019
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
