scholarly journals Product of parabolic cylinder functions involving Laplace transforms of confluent hypergeometric functions

2016 ◽  
Vol 27 (3) ◽  
pp. 181-196 ◽  
Author(s):  
Ridha Nasri
Keyword(s):  
Hypergeometric Functions ◽  
Laplace Transforms ◽  
Parabolic Cylinder ◽  
Confluent Hypergeometric Functions ◽  
Parabolic Cylinder Functions

scholarly journals Distributions of the Ratio and Product of Two Independent Weibull and Lindley Random Variables

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
N. J. Hassan ◽  
A. Hawad Nasar ◽  
J. Mahdi Hadad
Keyword(s):  
Hypergeometric Functions ◽  
Special Functions ◽  
Random Variables ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Parabolic Cylinder ◽  
Generalized Hypergeometric Functions ◽  
Confluent Hypergeometric Functions ◽  
Parabolic Cylinder Functions ◽  
The Moment

In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables. The moment generating functions (MGF) and the k-moment are driven from the ratio and product cases. In these derivations, we use some special functions, for instance, generalized hypergeometric functions, confluent hypergeometric functions, and the parabolic cylinder functions. Finally, we draw the PDF and CDF in many values of the parameters.

Asymptotic expansions and converging factors IV. Confluent hypergeometric, parabolic cylinder, modified Bessel, and ordinary Bessel functions

1959 ◽  
Vol 249 (1257) ◽  
pp. 270-283 ◽  
Keyword(s):  
Exponential Type ◽  
Asymptotic Expansions ◽  
Hypergeometric Functions ◽  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Modified Bessel Functions ◽  
Confluent Hypergeometric Functions ◽  
Special Cases ◽  
Parabolic Cylinder Functions

A theory of confluent hypergeometric functions is developed, based upon the methods described in the first three papers (I, II and III) of this series for replacing the divergent parts of asymptotic expansions by easily calculable series involving one or other of the four ‘ basic converging factors ’ which were investigated and tabulated in I. This theory is then illustrated by application to the special cases of exponential-type integrals, parabolic cylinder functions, modified Bessel functions, and ordinary Bessel functions.

scholarly journals On the Roots of Confluent Hypergeometric Functions

1914 ◽  
Vol 33 ◽  
pp. 48-64 ◽  
Author(s):  
Archd Milne
Keyword(s):  
Hypergeometric Functions ◽  
Graphical Form ◽  
Parabolic Cylinder ◽  
Confluent Hypergeometric Functions ◽  
Special Values ◽  
Parabolic Cylinder Functions ◽  
Class Of Functions

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. By giving special values to k and m it is then exemplified how the roots of other functions expressible in terms of Wk, m(z) may be studied. The zeros of the parabolic cylinder functions are then discussed. Some of the properties of an allied class of functions, denoted by ψn(z), are then given, and finally, it is shewn how the properties of Abel's function φm(z) may be obtained from results already given.

scholarly journals New Laplace transforms of Kummer’s confluent hypergeometric functions

2012 ◽  
Vol 55 (3-4) ◽  
pp. 1068-1071 ◽  
Author(s):  
Yong Sup Kim ◽  
Arjun K. Rathie ◽  
Djurdje Cvijović
Keyword(s):  
Hypergeometric Functions ◽  
Laplace Transforms ◽  
Confluent Hypergeometric Functions

scholarly journals A study of generalized summation theorems for the series 2F1 with an applications to Laplace transforms of convolution type integrals involving Kummer's functions 1F1

2018 ◽  
Vol 12 (1) ◽  
pp. 257-272
Author(s):  
Gradimir Milovanovic ◽  
Rakesh Parmar ◽  
Arjun Rathie
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Integral Transform ◽  
Laplace Transforms ◽  
Confluent Hypergeometric Function ◽  
Convolution Type ◽  
Product Theorem ◽  
Confluent Hypergeometric Functions

Motivated by recent generalizations of classical theorems for the series 2F1 [Integral Transform. Spec. Funct. 229(11), (2011), 823-840] and interesting Laplace transforms of Kummer's confluent hypergeometric functions obtained by Kim et al. [Math. Comput. Modelling 55 (2012), 1068-1071], first we express generalized summations theorems in explicit forms and then by employing these, we derive various new and useful Laplace transforms of convolution type integrals by using product theorem of the Laplace transforms for a pair of Kummer's confluent hypergeometric function.

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