scholarly journals A Note on Certain Laplace Transforms of Convolution-Type Integrals Involving Product of Two Generalized Hypergeometric Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Arjun Kumar Rathie ◽  
Young Hee Geum ◽  
Hwajoon Kim
Keyword(s):  
Hypergeometric Functions ◽  
Research Result ◽  
Research Paper ◽  
Laplace Transforms ◽  
Convolution Type ◽  
Generalized Hypergeometric Functions

The aim of this research paper is to provide as many as forty-five attractive Laplace transforms of convolution type related to the product of generalized hypergeometric functions. These are achieved by employing summation theorems for the series pFp−1 (for p = 2,3,4 , and 5) available in the literature. The obtained research result is to provide an easier method than the existing method.

scholarly journals Certain Laplace transforms of convolution type integrals involving product of two special pFp functions

2018 ◽  
Vol 51 (1) ◽  
pp. 264-276
Author(s):  
Gradimir V. Milovanović ◽  
Rakesh K. Parmar ◽  
Arjun K. Rathie
Keyword(s):  
Hypergeometric Functions ◽  
Discrete Math ◽  
Laplace Transforms ◽  
Convolution Type ◽  
Generalized Hypergeometric Functions ◽  
Kummer’S Function

Abstract Recently the authors obtained several Laplace transforms of convolution type integrals involving Kummer’s function 1F1 [Appl. Anal. Discrete Math., 2018, 12(1), 257-272]. In this paper, the authors aim at presenting several new and interesting Laplace transforms of convolution type integrals involving product of two special generalized hypergeometric functions pFp by employing classical summation theorems for the series 2F1, 3F2, 4F3 and 5F4 available in the literature.

scholarly journals Two dimensional Laplace transforms of generalized hypergeometric functions

1988 ◽  
Vol 11 (1) ◽  
pp. 167-175 ◽  
Author(s):  
R. S. Dahiya ◽  
I. H. Jowhar
Keyword(s):  
Hypergeometric Functions ◽  
Laplace Transforms ◽  
Two Dimensional ◽  
Generalized Hypergeometric Functions

The object of this paper is to obtain new operational relations between the original and the image functions that involve generalized hypergeometricG-functions.

scholarly journals The Integral Mittag-Leffler, Whittaker and Wright Functions

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3255
Author(s):  
Alexander Apelblat ◽  
Juan Luis González-Santander
Keyword(s):  
Closed Form ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Laplace Transforms ◽  
Graphical Form ◽  
Generalized Hypergeometric Functions ◽  
Infinite Sums ◽  
First Time ◽  
Mathematical Literature

Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters.

scholarly journals On several new Laplace transforms of generalized hypergeometric functions 2F2(x)

2021 ◽  
Vol 39 (4) ◽  
pp. 97-109
Author(s):  
Asmaa Orabi Mohammed ◽  
Medhat A. Rakha ◽  
Mohammed M. Awad ◽  
Arjun K. Rathie
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Laplace Transforms ◽  
Theoretical Physics ◽  
Generalized Hypergeometric Function ◽  
Generalized Hypergeometric Functions ◽  
Special Cases ◽  
And Mathematics

By employing generalizations of Gauss's second, Bailey's and Kummer's summation theorems obtained earlier by Rakha and Rathie, we aim to establish unknown Laplace transform of six rather general formulas of generalized hypergeometric function 2F2[a,b;c,d;x]. The results obtained in this paper are simple, interesting, easily established and may be useful in theoretical physics, engineering and mathematics. Results obtained earlier by Kim et al. and Choi and Rathie follow special cases of our main findings.

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.

scholarly journals General Summation Formulas Contiguous to the q-Kummer Summation Theorems and Their Applications

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1102
Author(s):  
Yashoverdhan Vyas ◽  
Hari M. Srivastava ◽  
Shivani Pathak ◽  
Kalpana Fatawat
Keyword(s):  
Hypergeometric Functions ◽  
Theory Theory ◽  
Binomial Theorem ◽  
Generalized Hypergeometric Functions ◽  
Quantum Calculus ◽  
The Third ◽  
Summation Formulas ◽  
Symmetric Quantum ◽  
Summation Theorem

This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.

Clebsh–Gordan coefficients for the algebra 𝔤𝔩₃ and hypergeometric functions

2021 ◽  
Vol 33 (1) ◽  
pp. 1-22
Author(s):  
D. Artamonov
Keyword(s):  
Explicit Formula ◽  
Lie Algebra ◽  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Content Type

The Clebsh–Gordan coefficients for the Lie algebra g l 3 \mathfrak {gl}_3 in the Gelfand–Tsetlin base are calculated. In contrast to previous papers, the result is given as an explicit formula. To obtain the result, a realization of a representation in the space of functions on the group G L 3 GL_3 is used. The keystone fact that allows one to carry the calculation of Clebsh–Gordan coefficients is the theorem that says that functions corresponding to the Gelfand–Tsetlin base vectors can be expressed in terms of generalized hypergeometric functions.

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