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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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Rarefied elliptic hypergeometric functions [PDF]
Advances in Mathematics, 2018 Two exact evaluation formulae for multiple rarefied elliptic beta integrals related to the simplest lens space are proved. They generalize evaluations of the type I and II elliptic beta integrals attached to the root system $C_n$. In a special $n=1$ case, the simplest $p\to 0$ limit is shown to lead to a new class of $q$-hypergeometric identities ...
Spiridonov, V.
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Inductance and hypergeometric functions
Journal of Computational and Applied Mathematics, 1991 AbstractVector potential and inductances for simple current distributions with rotational symmetry are considered. The approach is in terms of those hypergeometric functions that yield the simplest expressions, rather than complete elliptic integrals. In particular, an integral for the self-inductance of a solenoid of arbitrary thickness and length is ...
Per W. Karlsson
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Starlike Hypergeometric Functions [PDF]
Proceedings of the American Mathematical Society, 1961 E. P. Merkes, W. T. Scott
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Hypergeometric Functions for Function Fields
Finite Fields and Their Applications, 1995 AbstractWe introduce and study analogues of hypergeometric functions in the setting of function fields over finite fields. We show analogues of the differential equations, integral representations, transformation formulae, and continued fractions and show how analogues of various special functions and orthogonal polynomials occur as their ...
Dinesh S. Thakur
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Exact Expressions for Kullback–Leibler Divergence for Univariate Distributions [PDF]
EntropyThe Kullback–Leibler divergence (KL divergence) is a statistical measure that quantifies the difference between two probability distributions. Specifically, it assesses the amount of information that is lost when one distribution is used to approximate ...
Victor Nawa, Saralees Nadarajah
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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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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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