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.
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.
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.
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.
| № | Author name | position | Name of organisation |
|---|---|---|---|
| 1 | Xasanov A.. | 1 | Namangan state university |
| 2 | Tolasheva Y.I. | 2 | Namangan state university |
| № | Name of reference |
|---|---|
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