Appell Hypergeometric Expansions of the Solutions of the General Heun Equation

A. M. Ishkhanyan

Результат исследований: Материалы для журналаСтатья

1 цитирование (Scopus)

Выдержка

Starting from a second-order Fuchsian differential equation having five regular singular points, an equation obeyed by a function proportional to the first derivative of the solution of the Heun equation, we construct several expansions of the solutions of the general Heun equation in terms of Appell generalized hypergeometric functions of two variables of the first kind. Several cases when the expansions reduce to those written in terms of simpler mathematical functions such as the incomplete Beta function or the Gauss hypergeometric function are identified. The conditions for deriving finite-sum solutions via termination of the series are discussed. In general, the coefficients of the expansions obey four-term recurrence relations; however, there exist certain choices of parameters for which the recurrence relations involve only two terms, though not necessarily successive. For such cases, the coefficients of the expansions are explicitly calculated and the general solution of the Heun equation is constructed in terms of the Gauss hypergeometric functions.

Язык оригиналаАнглийский
Страницы (с-по)445-459
Число страниц15
ЖурналConstructive Approximation
Том49
Номер выпуска3
DOI
СостояниеОпубликовано - 15 июн 2019

Отпечаток

Heun Equation
Gauss Hypergeometric Function
Recurrence relation
Incomplete beta Function
Generalized Hypergeometric Function
Coefficient
Term
Singular Point
General Solution
Termination
Directly proportional
Differential equation
Derivative
Series
Differential equations
Derivatives

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics

Цитировать

Appell Hypergeometric Expansions of the Solutions of the General Heun Equation. / Ishkhanyan, A. M.

В: Constructive Approximation, Том 49, № 3, 15.06.2019, стр. 445-459.

Результат исследований: Материалы для журналаСтатья

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