Certain continued fraction representations for functions associated with mock theta functions of order three. (Q1872585)

As clearly expressed in the title, the author derives in this paper a number of continued fraction representations for functions associated with mock theta functions of order three. It is known that for \(a_2 \Phi_1 [a,b;c;z]\), when \(z\) and \(a,b,c\) take a particular form, continued fraction representations exist, but the same is not known for \(a_2 \Phi_1 [a,b;c;z]_m\). After revising the usual hypergeometric notations, the author gives the definitons of partial mock theta functions of order three, six and Jacobi's theta function. He then obtains an identity connecting partial series of the type \(\sum_{n=0}^m ((\alpha)_n z^n / (\beta)_n)\), and afterwards an infinite continued fraction representation for the same. Moreover, a finite continued fraction representation is also provided, together with certain special cases of the previous results. The paper finishes with concluding remarks by the author, who anounces a further communication with similar results for the fifth and seventh order mock theta functions.