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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The generalized confluent hypergeometric function [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1992 This article extends the theory of generalized hypergeometric functions of Gelfand and others to those including the case corresponding the classical confluent hypergeometric functions. Let \(Z_{r,n}\) be the set of \(r\times n\) complex matrices of maximal rank.
Kimura, Hironobu +2 more
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On the maximum value of a confluent hypergeometric function [PDF]
Comptes Rendus. Mathématique, 2022 We study the maximum value of the confluent hypergeometric function with oscillatory conditions of parameters. As a consequence, we obtain new inequalities for the Gauss hypergeometric function.
Fejzullahu, Bujar Xh.
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Fractional Integral of the Confluent Hypergeometric Function Related to Fuzzy Differential Subordination Theory [PDF]
Fractal and Fractional, 2022 The fuzzy differential subordination concept was introduced in 2011, generalizing the concept of differential subordination following a recent trend of adapting fuzzy sets theory to other already-established theories.
Mugur Acu +2 more
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Relations between Confluent Hypergeometric Functions [PDF]
Proceedings of the National Academy of Sciences, 1931 Some of the functions mentioned in a recent paper may be expressed in terms of known functions.
H. Bateman
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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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Properties of the confluent hypergeometric function [PDF]
Journal of Mathematics and Physics, 1948 GRSN 255639"November 18, 1948."Includes bibliographical references.Supported by the Army Signal Corps, the Navy Department (Office of Naval Research) and the Air Force (Air Material Command) under Signal Corps.
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Study on new integral operators defined using confluent hypergeometric function [PDF]
Advances in Difference Equations, 2021 Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function.
Georgia Irina Oros
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Multivariate Generalization of the Confluent Hypergeometric Function Kind 1 Distribution [PDF]
International Journal of Mathematics and Mathematical Sciences, 2008 The confluent hypergeometric function kind 1 distribution with the probability density function (pdf) proportional to x_−1F11(α;β;−x), x>0 occurs as the distribution of the ratio of independent gamma and beta variables.
Daya K. Nagar +1 more
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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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