scholarly journals MORE SPECIAL FUNCTIONS TRAPPED

2013 ◽  
Vol 24 (02) ◽  
pp. 1350004
Author(s):  
CHARLES SCHWARTZ
Keyword(s):  
Hypergeometric Function ◽  
Bessel Functions ◽  
Special Functions ◽  
Mathematical Physics ◽  
Confluent Hypergeometric Function ◽  
Trapezoidal Rule ◽  
Integral Representations ◽  
Gamma Functions ◽  
Incomplete Gamma Functions

We extend the technique of using the trapezoidal rule for efficient evaluation of the special functions of mathematical physics given by integral representations. This technique was recently used for Bessel functions, and here we treat incomplete gamma functions and the general confluent hypergeometric function.

scholarly journals NUMERICAL CALCULATION OF BESSEL FUNCTIONS

2012 ◽  
Vol 23 (12) ◽  
pp. 1250084 ◽  
Author(s):  
CHARLES SCHWARTZ
Keyword(s):  
Numerical Calculation ◽  
Bessel Functions ◽  
Special Functions ◽  
Computational Procedure ◽  
Mathematical Physics ◽  
Trapezoidal Rule ◽  
Integral Representations ◽  
The Many

A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The trapezoidal rule, applied to suitable integral representations, may become the method of choice for evaluation of the many special functions of mathematical physics.

scholarly journals Certain investigations in the field of special functions

2020 ◽  
Vol 1 (1) ◽  
pp. 87-98
Author(s):  
Maisoon A. Kulib ◽  
Ahmed A. Al-Gonah ◽  
Salem S. Barahmah
Keyword(s):  
Hypergeometric Function ◽  
Special Functions ◽  
Beta Function ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Confluent Hypergeometric Functions ◽  
Research Fields ◽  
Summation Formulas ◽  
Physical Problems ◽  
Wide Range

Motivated mainly by a variety of applications of Euler's Beta, hypergeometric, and confluent hypergeometric functions together with their extensions in a wide range of research fields such asengineering, chemical, and physical problems. In this paper, we introduce modified forms of some extended special functions such as Gamma function, Beta function, hypergeometric function and confluent hypergeometric function by making use of the idea given in reference \cite{9}. Also, certain investigations including summation formulas, integral representations and Mellin transform of these modified functions are derived. Further, many known results are obtained asspecial cases of our main results.

scholarly journals A study on certain properties of generalized special functions defined by Fox-Wright function

2020 ◽  
Vol 5 (1) ◽  
pp. 147-162
Author(s):  
Enes Ata ◽  
İ. Onur Kıymaz
Keyword(s):  
Hypergeometric Function ◽  
Special Functions ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Summation Formulas ◽  
Frequent Use ◽  
Derivative Formulas ◽  
Transformation Formulas

AbstractIn this study, motivated by the frequent use of Fox-Wright function in the theory of special functions, we first introduced new generalizations of gamma and beta functions with the help of Fox-Wright function. Then by using these functions, we defined generalized Gauss hypergeometric function and generalized confluent hypergeometric function. For all the generalized functions we have defined, we obtained their integral representations, summation formulas, transformation formulas, derivative formulas and difference formulas. Also, we calculated the Mellin transformations of these functions.

scholarly journals New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Pshtiwan Othman Mohammed ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Artion Kashuri ◽  
Faraidun Hamasalh ◽  
...  
Keyword(s):  
Convex Functions ◽  
Special Functions ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Gamma Functions ◽  
Incomplete Gamma Functions ◽  
Type Integral

AbstractA specific type of convex functions is discussed. By examining this, we investigate new Hermite–Hadamard type integral inequalities for the Riemann–Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.

scholarly journals On the Volterra-Type Fractional Integro-Differential Equations Pertaining to Special Functions

2020 ◽  
Vol 4 (3) ◽  
pp. 33
Author(s):  
Yudhveer Singh ◽  
Vinod Gill ◽  
Jagdev Singh ◽  
Devendra Kumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Hypergeometric Function ◽  
Fractional Order ◽  
Integral Transform ◽  
Special Functions ◽  
Confluent Hypergeometric Function ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Volterra Type

In this article, we apply an integral transform-based technique to solve the fractional order Volterra-type integro-differential equation (FVIDE) involving the generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function in terms of several complex variables in the kernel. We also investigate and introduce the Elazki transform of Hilfer-derivative, generalized Lorenzo-Hartely function and generalized Lauricella confluent hypergeometric function. In this article, we have established three results that are present in the form of lemmas, which give us new results on the above mentioned three functions, and by using these results we have derived our main results that are given in the form of theorems. Our main results are very general in nature, which gives us some new and known results as a particular case of results established here.

Special functions, infinite divisibility and transcendental equations

1979 ◽  
Vol 85 (3) ◽  
pp. 453-464 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
C. Ping May
Keyword(s):  
Bessel Functions ◽  
Special Functions ◽  
Infinite Divisibility ◽  
Probability Density Functions ◽  
Integral Representations ◽  
Density Functions ◽  
Modified Bessel Functions ◽  
Explicit Formulas ◽  
Linear Combinations ◽  
Transcendental Equations

AbstractWe establish integral representations for quotients of Tricomi ψ functions and of several quotients of modified Bessel functions and of linear combinations of them. These integral representations are used to prove the complete monotonicity of the functions considered and to prove the infinite divisibility of a three parameter probability distribution. Limiting cases of this distribution are the hitting time distributions considered recently by Kent and Wendel. We also derive explicit formulas for the Kent–Wendel probability density functions.

scholarly journals On the integral representations for the confluent hypergeometric function

2016 ◽  
Vol 472 (2193) ◽  
pp. 20160421 ◽  
Author(s):  
Bujar Xh. Fejzullahu
Keyword(s):  
Integral Representation ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Confluent Hypergeometric Function ◽  
Integral Representations ◽  
Contour Integral ◽  
Confluent Hypergeometric Functions ◽  
Special Cases

In this paper, we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases. Consequently, we derive expansions of the confluent hypergeometric function in terms of functions of the same kind. Furthermore, we obtain a new identity involving integrals and sums of confluent hypergeometric functions. Our results generalized several well-known results in the literature.

scholarly journals Analytical and asymptotic evaluations of Dawson’s integral and related functions in mathematical physics

2019 ◽  
Vol 25 (2) ◽  
pp. 179-188
Author(s):  
Victor Nijimbere
Keyword(s):  
Asymptotic Expansion ◽  
Hypergeometric Function ◽  
Complex Plane ◽  
Asymptotic Expansions ◽  
Error Function ◽  
Mathematical Physics ◽  
Confluent Hypergeometric Function ◽  
Dispersion Function ◽  
Plasma Dispersion

Abstract Dawson’s integral and related functions in mathematical physics that include the complex error function (Faddeeva’s integral), Fried–Conte (plasma dispersion) function, Jackson function, Fresnel function and Gordeyev’s integral are analytically evaluated in terms of the confluent hypergeometric function. And hence, the asymptotic expansions of these functions on the complex plane {\mathbb{C}} are derived by using the asymptotic expansion of the confluent hypergeometric function.

Sign in / Sign up

Export Citation Format

Share Document