appell function
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Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2141
Author(s):  
Poonam Sharma ◽  
Ravinder Krishna Raina ◽  
Janusz Sokół

Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.


2020 ◽  
pp. 1-13
Author(s):  
David C. Bowie

Abstract This note derives analytic expressions for annuities based on a class of parametric mortality “laws” (the so-called Makeham–Beard family) that includes a logistic form that models a decelerating increase in mortality rates at the higher ages. Such models have been shown to provide a better fit to pensioner and annuitant mortality data than those that include an exponential increase. The expressions derived for evaluating single life and joint life annuities for the Makeham–Beard family of mortality laws use the Gauss hypergeometric function and Appell function of the first kind, respectively.


2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
D. L. Suthar ◽  
Mengesha Ayene

The aim of this paper is to deal with two integral transforms involving the Appell function as their kernels. We prove some compositions formulas for generalized fractional integrals with k-Bessel function. The results are expressed in terms of generalized Wright type hypergeometric function and generalized hypergeometric series. Also, the authors presented some related assertion for Saigo, Riemann-Liouville type, and Erdélyi-Kober type fractional integral transforms.


2017 ◽  
Vol 28 (9) ◽  
pp. 629-644 ◽  
Author(s):  
Yu. A. Brychkov ◽  
Nasser Saad
Keyword(s):  

2017 ◽  
Vol 37 (1) ◽  
pp. 169-176
Author(s):  
Rakesh K. Parmar ◽  
Sunil Dutt Purohit

Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing (presumably new) a generating function for the extended second Appell hypergeometric function $F_{2} (a, b, b'; c, c'; x, y; p)$. Further we derive a relation in terms of the Laguerre polynomials and differentiation formulas. We also present special cases of the main results of this paper.


2016 ◽  
Vol 31 (1) ◽  
pp. 115-129 ◽  
Author(s):  
Junesang Choi ◽  
Jitendra Daiya ◽  
Dinesh Kumar ◽  
Ram Kishore Saxena

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