The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummers second transformation for the confluent hypergeometric function ${}_1F_1$ using a differential equation approach.
We give an elementary proof that Davies definition of a solution to a rough differential equation and the notion of solution given by Bailleul in (Flows driven by rough paths) coincide. This provides an alternative point on view on the deep algebraic insights of Cass and Weidner in their work (Tree algebras over topological vector spaces in rough path theory).
A silting theorem was established by Buan and Zhou as a generalisation of the classical tilting theorem of Brenner and Butler. In this paper, we give an alternative proof of the theorem by using differential graded algebras.
In this note, we aim to provide generalizations of (i) Knuths old sum (or Reed Dawson identity) and (ii) Riordans identity using a hypergeometric series approach.
We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay) solutions for these systems.
S. Kodavanji
,A. K. Rathie
,R. B. Paris
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(2015)
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"A derivation of two transformation formulas contiguous to that of Kummers second theorem via a differential equation approach"
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Richard Paris
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