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Anand Kumar Srivastava ¹, Gopendra Kumar ², D. Bhattacharya ³

Affiliations
1 Department of Geology, Lucknow University, Lucknow, IN
2 48 Pandariba, Lucknow - 226 004, IN
3 AMD/DAE, NR, West Block - 7, R K Puram, New Delhi - 110 066, IN

Abstract

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Anand Kumar Srivastava ¹

Affiliations
1 Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, IN

Abstract

In two of our early papers we have studied a number of transformations connecting “partial series” derived from the mock theta functions of order 3, 5 and 7. It has been shown therein that the transformations of partial mock theta functions give valuable information regarding their structure. These transformations have also brought out new relationships between ‘partial’ and ‘complete’ mock theta functions which thus far were not known.

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Anand Kumar Srivastava ¹

Affiliations
1 Department of Mathematics and Astronomy, Lucknow University, Lucknow-226007, IN

Abstract

In a recent paper [3, 3.10-3.23, 6§] we have defined partial mock theta functions of order three and have shown how they are interrelated to each other.
The object of this paper is to define partial mock theta functions of orders 5 and 7. Unlike mock theta functions of order three, the mock theta functions of orders 5 and 7 have no direct basic hypergeometric definitions, although they have been shown to be limiting cases of certain ₃Φ₂ and ₄Φ₃ series, respectively, (see Anju Gupta [2, 152-161) and R.P. Agarwal [1, 99-101]). To avoid the limiting process we have defined the partial mock theta functions of orders five and seven as the partial series of the corresponding infinite series definitions, as given by Ramanujan.

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