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EVALUATION OF THE NON-ELEMENTARY INTEGRAL \(\int e^{\lambda x^\alpha}dx\), \(\alpha\ge 2\), AND OTHER RELATED INTEGRALS [PDF]
Ural Mathematical Journal, 2017 A formula for the non-elementary integral \(\int e^{\lambda x^\alpha} dx\) where \(\alpha\) is real and greater or equal two, is obtained in terms of the confluent hypergeometric function \(_{1}F_1\) by expanding the integrand as a Taylor series.
Victor Nijimbere
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Some Inequalities of Extended Hypergeometric Functions
Mathematics, 2021 Hypergeometric functions and their inequalities have found frequent applications in various fields of mathematical sciences. Motivated by the above, we set up certain inequalities including extended type Gauss hypergeometric function and confluent ...
Shilpi Jain +3 more
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AIMS Mathematics, 2022 In this paper, we mainly prove monotonicity and convexity properties of certain functions involving zero-balanced Gaussian hypergeometric function F(a,b;a+b;x).
Ye-Cong Han, Chuan-Yu Cai, Ti-Ren Huang
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International Journal of Mathematics for Industry, 2023 Fractional kinetic equations are of immense importance in describing and solving numerous intriguing problems of physics and astrophysics. Inequalities are important topics in special functions.
Ankita Chandola, Rupakshi Mishra Pandey
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Investigation of Fractional Calculus for Extended Wright Hypergeometric Matrix Functions
Abstract and Applied Analysis, 2023 Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integral equations ...
Mohamed Niyaz +2 more
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Mathematics, 2022 Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol.
Ahmed Bakhet +4 more
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HYPERGEOMETRIC ZETA FUNCTIONS [PDF]
International Journal of Number Theory, 2010 This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers.
Hassen, Abdul, Nguyen, Hieu D.
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Expansions of Hypergeometric Functions in Hypergeometric Functions [PDF]
Mathematics of Computation, 1961 In [1] Luke gave an expansion of the confluent hypergeometric function in terms of the modified Bessel functions I v ( z ) {I_v}(z) . The existence of other, similar expansions implied that more general expansions might exist. Such was the case.
Fields, J. L., Wimp, J.
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A parafermionic hypergeometric function and supersymmetric 6j-symbols
Nuclear Physics B, 2023 We study properties of a parafermionic generalization of the hyperbolic hypergeometric function appearing as the most important part in the fusion matrix for Liouville field theory and the Racah-Wigner symbols for the Faddeev modular double. We show that
Elena Apresyan +2 more
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Cumhuriyet Science Journal, 2022 When the literature is examined, it is seen that there are many studies on the generalizations of gamma, beta and hypergeometric functions. In this paper, new types of generalized gamma and beta functions are defined and examined using the Wright ...
Enes Ata, İ. Onur Kıymaz
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