Results 11 to 20 of about 527,794 (256)
Evaluation of the non-elementary integral $\int e^{\lambda x^\alpha} dx, \alpha\ge2$, 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 $_1F_1$. This result is verified by directly evaluating the area under
Nijimbere, Victor
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A physicist's guide to the solution of Kummer's equation and confluent hypergeometric functions [PDF]
Condensed Matter Physics, 2022 The confluent hypergeometric equation, also known as Kummer's equation, is one of the most important differential equations in physics, chemistry, and engineering. Its two power series solutions are the Kummer function, M(a,b,z), often referred to as the
W. N. Mathews Jr. +3 more
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Applications of Confluent Hypergeometric Function in Strong Superordination Theory [PDF]
Axioms, 2022 In the research presented in this paper, confluent hypergeometric function is embedded in the theory of strong differential superordinations. In order to proceed with the study, the form of the confluent hypergeometric function is adapted taking into ...
Georgia Irina Oros +2 more
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Turán type inequalities for Tricomi confluent hypergeometric functions [PDF]
Constructive Approximation 37(2) (2013) 195-221, 2011 Some sharp two-sided Tur\'an type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher ...
Árpád Baricz, Mourad E. H. Ismail
arxiv +3 more sources
On the zeros of certain confluent hypergeometric functions [PDF]
Proceedings of the American Mathematical Society, 1973 The theory of continued fractions is used to derive the following results which hold for − 1 2 > α > ∞ - \tfrac {1}{2} > \alpha > \infty : (1) If \[ 1 F 1
Pam Wynn
+4 more sources
On the Roots of Confluent Hypergeometric Functions [PDF]
Proceedings of the Edinburgh Mathematical Society, 1914 In the present paper the disposition of the roots of the confluent hypergeometric functions — denoted by Wk, m(z) — as affected by changing the parameters k and m is investigated. The results are then shewn in a graphical form, and various typical illustrations of the functions are given.
Archd Milne
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Derivatives of Horn-type hypergeometric functions with respect to their parameters [PDF]
arXiv, 2017 We consider the derivatives of Horn hypergeometric functions of any number variables with respect to their parameters. The derivative of the function in $n$ variables is expressed as a Horn hypergeometric series of $n+1$ infinite summations depending on ...
Bytev, V., Kniehl, B., Moch, S.
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Quadratic relations for confluent hypergeometric functions [PDF]
Tohoku Mathematical Journal, 2000 We present a theory of intersection on the complex projective line for homology and cohomology groups defined by connections which are regular or not. We apply this theory to confluent hypergeometric functions, and obtain, as an analogue of period relations, quadratic relations satisfied by confluent hypergeometric functions.
Majima, Hideyuki +2 more
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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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Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
Kuwait Journal of Science, 2023 The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper.
Gradimir V. Milovanović +2 more
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