346

В этой статье рассматривается новая взаимосвязь между гипергеометрической функцией Аппеля
(
)
1 1 2
F a;b ,b ;c; x, y и функцией Кампе де Фериет F44;3;4,3,4 [x, y] .  Рассмотрено метод разложение на ряд гипергеометрической функции Аппеля, а также использовано метод группировки членов  равномерно сходящегося степенного ряда.  Из полученного соотношения получено, что существуют связь между функциями Гаусса, обобщенной гипергеометрической функцией 8 F7(x4) и гиперболическими косинусами.

  • Internet ҳавола
  • DOI
  • UzSCI тизимида яратилган сана 18-10-2022
  • Ўқишлар сони 0
  • Нашр санаси 11-02-2022
  • Мақола тилиRus
  • Саҳифалар сони6-14
Ўзбек

Мақолада Аппелнинг ( )
1 1 2
F a;b ,b ;c; x, y гипергеометрик функцияси ва Кампе де Фериетнинг F44;3;4,3,4 [x, y] функцияси орасидаги янги муносабат олинган. Бунда Аппелнинг гипергеометрик функциясининг қаторга ёйилмасидан ҳамда текис яқинлашувчи даражали қаторларнинг ҳадларини группалаш усулидан фойдаланилган. Олинган муносабатдан Гаусс функциялари, умумлашган гипергеометрик 8 F7(x4) функция ва гиперболик косинуслар ўртасидаги боғланишлар мавжудлиги аниқланган.

Русский

В этой статье рассматривается новая взаимосвязь между гипергеометрической функцией Аппеля
(
)
1 1 2
F a;b ,b ;c; x, y и функцией Кампе де Фериет F44;3;4,3,4 [x, y] .  Рассмотрено метод разложение на ряд гипергеометрической функции Аппеля, а также использовано метод группировки членов  равномерно сходящегося степенного ряда.  Из полученного соотношения получено, что существуют связь между функциями Гаусса, обобщенной гипергеометрической функцией 8 F7(x4) и гиперболическими косинусами.

English

In this paper, we get a new relationship between Appel’s hypergeometric function F1 (a;b1,b2;c; x, y) and Campe de Feriet’s function 4;4,4 [ ]
4;3,3
F x, y . We use expansion of series Appel's hypergeometric function and the method of grouping terms of smooth convergent power series.  We find connections between Gaussian functions, generalized hypergeometric function 4
8 7
F (x ) and hyperbolic cosines by using new relationship.

Муаллифнинг исми Лавозими Ташкилот номи
1 Xasanov A.. 1 Namangan state university
2 Tolasheva Y.I. 2 Namangan state university
Ҳавола номи
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