scholarly journals A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations

2021 ◽  
Vol 499 (2) ◽  
pp. 125037
Author(s):  
D.Yu. Melikdzhanian ◽  
A.M. Ishkhanyan
Keyword(s):  
Hypergeometric Solutions

scholarly journals Generalized-Hypergeometric Solutions of the General Fuchsian Linear ODE Having Five Regular Singularities

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 102 ◽  
Author(s):  
Ishkhanyan ◽  
Cesarano
Keyword(s):  
Differential Equation ◽  
Hypergeometric Function ◽  
Singular Points ◽  
Polynomial Equations ◽  
Generalized Hypergeometric Function ◽  
Characteristic Exponents ◽  
Linear Ode ◽  
Hypergeometric Solutions

We show that a Fuchsian differential equation having five regular singular points admits solutions in terms of a single generalized hypergeometric function for infinitely many particular choices of equation parameters. Each solution assumes four restrictions imposed on the parameters: two of the singularities should have non-zero integer characteristic exponents and the accessory parameters should obey polynomial equations.

scholarly journals q-Hypergeometric solutions of q-difference equations

1999 ◽  
Vol 194 (1-3) ◽  
pp. 3-22 ◽  
Author(s):  
Sergei A. Abramov ◽  
Peter Paule ◽  
Marko Petkovšek
Keyword(s):  
Difference Equations ◽  
Hypergeometric Solutions

scholarly journals m-Fold Hypergeometric Solutions of Linear Recurrence Equations Revisited

2012 ◽  
Vol 6 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Peter Horn ◽  
Wolfram Koepf ◽  
Torsten Sprenger
Keyword(s):  
Linear Recurrence ◽  
Recurrence Equations ◽  
Hypergeometric Solutions
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