Results 1 to 10 of about 12,057 (258)

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
doaj   +4 more sources

Confluent Hypergeometric Functions [PDF]

Nature, 1960
Confluent Hypergeometric Functions By Dr. L. J. Slater. Pp. ix + 247. (Cambridge: At the University Press, 1960.) 65s. net.
W. N. Bailey
  +6 more sources

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, Gheorghe Oros, Ancuța Maria Rus   +2 more
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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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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

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.
Hideyuki Majima, Kenji Matsumoto, Nobuki Takayama   +2 more
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Exact Expressions for Kullback–Leibler Divergence for Univariate Distributions [PDF]

Entropy
The 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
doaj   +2 more sources

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, Arjun K. Rathie, Nevena M. Vasović   +2 more
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On the zeros of a confluent hypergeometric function [PDF]

Proceedings of the American Mathematical Society, 1965
Jet Wimp
  +4 more sources

Properties of the Confluent Hypergeometric Function [PDF]

Journal of Mathematics and Physics, 1949
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.
openaire   +5 more sources