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

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Department of General Physics, Russian-Armenian University, Yerevan 0051, Armenia
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Matter Wave Physics Department, Institute for Physical Research, Ashtarak 0203, Armenia
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Section of Mathematics-International Telematic University Uninettuno, C.so Vittorio Emanuele II, 39, 00186 Roma, Italy
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Author to whom correspondence should be addressed.
Axioms 2019, 8(3), 102; https://doi.org/10.3390/axioms8030102
Received: 23 June 2019 / Revised: 3 August 2019 / Accepted: 27 August 2019 / Published: 2 September 2019
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. View Full-Text
Keywords: Fuchsian equation; generalized hypergeometric function; recurrence relation Fuchsian equation; generalized hypergeometric function; recurrence relation
MDPI and ACS Style

Ishkhanyan, A.; Cesarano, C. Generalized-Hypergeometric Solutions of the General Fuchsian Linear ODE Having Five Regular Singularities. Axioms 2019, 8, 102.

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