On Generalized Mock Theta Functions of Tenth Order
DOI:
https://doi.org/10.48048/tis.2022.2070Keywords:
Mock theta functions, q-hypergeometric series, Continued fraction, q-integrals, Multibasic expansionAbstract
In this paper we have given 3 independent variable generalization of tenth order mock theta functions and have found some relations between generalized mock theta functions of different order. We have given a continued fraction representation of generalized tenth order mock theta functions. We have also given the q-integral representation and multibasic expansion for these functions. Further by specializing the parameters we have connected mock theta functions with continued fraction of Ramanujan.
HIGHLIGHTS
- Mock theta functions are last gift to mathematics by Ramanujan. These functions are also called mysterious functions as the exact meaning of order of mock theta functions is mystery for mathematicians
- The generalization of tenth order mock theta functions connects them with different order mock theta functions and with Ramanujan’s continued fractions
- The specialization of parameters of generalized mock theta functions gives the famous Ramanujan’s continued fraction
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