http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ON THE COMPUTATIONS OF CONTIGUOUS RELATIONS FOR <sub>2</sub>F<sub>1</sub> HYPERGEOMETRIC SERIES
Rakha, Medhat A.,Ibrahim, Adel K.,Rathie, Arjun K. Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.2
Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form $_2F_1$[$a_1$, $a_2$; $a_3$; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters $a_1$, $a_2$ and $a_3$. We also, discussed the existence condition of our formula.
Extensions of Euler type II transformation and Saalsch[문자]tz's theorem
Medhat A. Rakha,Arjun K. Rathie 대한수학회 2011 대한수학회보 Vol.48 No.1
In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalsch[문자]tz's summation theorem for the series _3F_2 has been investigated. Two interesting applications of the newly obtained extension of classical Saalsch[문자]tz's summation theorem are given.
EXTENSIONS OF EULER TYPE II TRANSFORMATION AND SAALSCHÜTZ'S THEOREM
Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2011 대한수학회보 Vol.48 No.1
In this research paper, motivated by the extension of the Euler type I transformation obtained very recently by Rathie and Paris, the authors aim at presenting the extensions of Euler type II transformation. In addition to this, a natural extension of the classical Saalsch$\ddot{u}$tz's summation theorem for the series $_3F_2$ has been investigated. Two interesting applications of the newly obtained extension of classical Saalsch$\ddot{u}$tz's summation theorem are given.
CERTAIN REDUCTION AND TRANSFORMATION FORMULAS FOR THE KAMPÉ DE FÉRIET FUNCTION
Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
In 2014, Liu and Wang established a large number of interesting reduction, transformation and summation formulas for the Kampé de Fériet function. Inspired by the work, we aim to find further several transformation and reduction formulas for the Kampé de Fériet function. Theses formulas are mainly based on the formulas given by Liu and Wang [33].
ON SEVERAL NEW CONTIGUOUS FUNCTION RELATIONS FOR k-HYPERGEOMETRIC FUNCTION WITH TWO PARAMETERS
Chinra, Sivamani,Kamalappan, Vilfred,Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3
Very recently, Mubeen, et al. [6] have obtained fifteen contiguous function relations for k-hypergeometric functions with one parameter by the same technique developed by Gauss. The aim of this paper is to obtain seventy-two new and interesting contiguous function relations for k-hypergeometric functions with two parameters. Obviously, for $k{\rightarrow}1$ we recover the results obtained by Cho, et al. [2] and Rakha, et al. [8].
NEW SERIES IDENTITIES FOR ${\frac{1}{\Pi}}$
Awad, Mohammed M.,Mohammed, Asmaa O.,Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4
In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems have been found interesting applications in obtaining various series identities for ${\Pi}$, ${\Pi}^2$ and ${\frac{1}{\Pi}}$. The aim of this research paper is to provide twelve general formulas for ${\frac{1}{\Pi}}$. On specializing the parameters, a large number of very interesting series identities for ${\frac{1}{\Pi}}$ not previously appeared in the literature have been obtained. Also, several other results for multiples of ${\Pi}$, ${\Pi}^2$, ${\frac{1}{{\Pi}^2}}$, ${\frac{1}{{\Pi}^3}}$ and ${\frac{1}{\sqrt{\Pi}}}$ have been obtained. The results are established with the help of the extensions of classical Gauss's summation theorem available in the literature.
ON AN INTERESTING EXTENSION OF KUMMER'S SECOND THEOREM WITH APPLICATIONS
Awad, Mohammed M.,Mohammed, Asmaa O.,Rakha, Medhat A.,Rathie, Arjun K. Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.1
In this research paper, an attempt has been made to provide an interesting extension of the well-known and useful Kummer's second theorem. Several applications have also been given.