Open AccessOn Generalized Mock Theta Functions of Tenth Order
Author(s) -
Pramod Kumar Rawat
Publication year - 2022
Publication title -
trends in sciences
Language(s) - English
Resource type - Journals
ISSN - 2774-0226
DOI - 10.48048/tis.2022.2070
Subject(s) - ramanujan's sum , ramanujan theta function , generalization , mathematics , representation (politics) , theta function , order (exchange) , pure mathematics , fraction (chemistry) , mathematical analysis , chemistry , organic chemistry , politics , political science , law , finance , economics
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