Publicado

2019-07-01

Generalized Bilateral Eighth Order Mock Theta Functions and Continued Fractions

Funciones Theta Mock generalizadas en dos variables de orden ocho

Palabras clave:

q-Hypergeometric series, Mock theta functions, Continued fraction (en)
funciones Theta Mock, fracción continuada, orden ocho en dos variables (es)

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Autores/as

  • Bhaskar Srivastava University of Lucknow
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.
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.

Citas

G. Gasper and M. Rahman, Basic Hypergeometric Series, Encycl. Math. Applics., Vol. 35, Cambridge University Press, Cambridge, 1990.

B. Gordon and R.J. McIntosh, Some eighth order mock theta functions, J. London Math. Soc. 62(2) (2000), 321-335.

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.

S. Ramanujan, Collected Papers, Cambridge University Press, Cambridge, 1927; reprinted by Chelsea, New York 1962; reprinted by the American Mathematical Society, Providence, RI, 2000.

L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. 54 (1952), 147-167.

Licencia

Derechos de autor 2020 Revista Colombiana de Matemáticas

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.