hypergeometric differential equation
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2021 ◽  
Vol 20 (1) ◽  
pp. 182-185
Author(s):  
Salah Hamd ◽  
Faisal Saleh Abdalla ◽  
Ahmed Shletiet

In this paper we consider a matrix Hypergeometric differential equation, which are special matrix functions and solution of a specific second order linear differential equation. The aim of this work is to extend a well known theorem on Hypergeometric  function in the complex plane to a matrix version, and we  show that  the asymptotic expansions of  Hypergeometric  function in the complex plane ” that are given in the literature are special members of our main result. Background and motivation are discussed.


2021 ◽  
Vol 157 (6) ◽  
pp. 1265-1301
Author(s):  
Shun Ohkubo

In the 1970s, Dwork defined the logarithmic growth (log-growth for short) filtrations for $p$ -adic differential equations $Dx=0$ on the $p$ -adic open unit disc $|t|<1$ , which measure the asymptotic behavior of solutions $x$ as $|t|\to 1^{-}$ . Then, Dwork calculated the log-growth filtration for $p$ -adic Gaussian hypergeometric differential equation. In the late 2000s, Chiarellotto and Tsuzuki proposed a fundamental conjecture on the log-growth filtrations for $(\varphi ,\nabla )$ -modules over $K[\![t]\!]_0$ , which can be regarded as a generalization of Dwork's calculation. In this paper, we prove a generalization of the conjecture to $(\varphi ,\nabla )$ -modules over the bounded Robba ring. As an application, we prove a generalization of Dwork's conjecture proposed by Chiarellotto and Tsuzuki on the specialization property for log-growth Newton polygons.


2020 ◽  
Vol 14 (3) ◽  
pp. 125-132
Author(s):  
Asad Ali ◽  
Mujahid Islam ◽  
Aqeela Noreen ◽  
Zaib-u- Nisa

2019 ◽  
Vol 22 (7) ◽  
pp. 1113-1121 ◽  
Author(s):  
Mámon Abu Hammad ◽  
Hamza Alzaareer ◽  
Hassan Al-Zoubi ◽  
Hemen Dutta

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