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Some new formulas for the Horns hypergeometric functions

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 Added by Ayman Shehata
 Publication date 2021
  fields
and research's language is English




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The aim of this work is to demonstrate various an interesting recursion formulas, differential and integral operators, integration formulas, and infinite summation for each of Horns hypergeometric functions $mathrm{H}_{1}$, $mathrm{H}_{2}$, $mathrm{H}_{3}$, $mathrm{H}_{4}$, $mathrm{H}_{5}$, $mathrm{H}_{6}$ and $mathrm{H}_{7}$ by the contiguous relations of Horns hypergeometric series. Some interesting different cases of our main consequences are additionally constructed.



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Inspired by the recent work Sahin and Agha gave recursion formulas for $mathcal{G}_{1}$ and $mathcal{G}_{2}$ Horn hypergeometric functions cite{saa}. The object of work is to establish several new recursion relations, relevant differential recursion formulas, new integral operators, infinite summations and interesting results for Horns hypergeometric functions $mathcal{G}_{1}$, $mathcal{G}_{2}$ and $mathcal{G}_{3}$.
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