scholarly journals Unified integrals involving product of multivariable polynomials and generalized Bessel functions

2019 ◽  
Vol 38 (6) ◽  
pp. 73-83
Author(s):  
K. S. Nisar ◽  
D. L. Suthar ◽  
Sunil Dutt Purohit ◽  
Hafte Amsalu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
General Character ◽  
Polynomial Functions ◽  
Finite Product ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Multivariable Polynomial ◽  
Integral Formulae

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

scholarly journals Inclusion of the Generalized Bessel Functions in the Janowski Class

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Saiful R. Mondal ◽  
Mohammed Al Dhuain
Keyword(s):  
Bessel Function ◽  
Unit Disk ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Generalized Bessel Function ◽  
Generalized Bessel Functions

Sufficient conditions on A, B, p, b, and c are determined that will ensure the generalized Bessel function up,b,c satisfies the subordination up,b,c(z)≺1+Az/(1+Bz). In particular this gives conditions for (-4κ/c)(up,b,c(z)-1), c≠0, to be close-to-convex. Also, conditions for up,b,c(z) to be Janowski convex and zup,b,c(z) to be Janowski starlike in the unit disk D=z∈C:z<1 are obtained.

scholarly journals CERTAIN NEW INTEGRAL FORMULAS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

2014 ◽  
Vol 51 (4) ◽  
pp. 995-1003 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal ◽  
Sudha Mathur ◽  
Sunil Dutt Purohit
Keyword(s):  
Bessel Functions ◽  
Integral Formulas ◽  
Generalized Bessel Functions

scholarly journals Unified integral associated with the generalized V-function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. Chandak ◽  
S. K. Q. Al-Omari ◽  
D. L. Suthar
Keyword(s):  
Bessel Function ◽  
Hypergeometric Function ◽  
Exponential Function ◽  
Special Functions ◽  
General Nature ◽  
Generalized Hypergeometric Function ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Special Cases ◽  
Lommel Function

Abstract In this paper, we present two new unified integral formulas involving a generalized V-function. Some interesting special cases of the main results are also considered in the form of corollaries. Due to the general nature of the V-function, several results involving different special functions such as the exponential function, the Mittag-Leffler function, the Lommel function, the Struve function, the Wright generalized Bessel function, the Bessel function and the generalized hypergeometric function are obtained by specializing the parameters in the presented formulas. More results are also discussed in detail.

Lemniscate convexity of generalized Bessel functions

2019 ◽  
Vol 56 (4) ◽  
pp. 404-419
Author(s):  
Vibha Madaan ◽  
Ajay Kumar ◽  
V. Ravichandran
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Generalized Bessel Functions

Abstract Sufficient conditions on associated parameters p, b and c are obtained so that the generalized and “normalized” Bessel function up(z) = up,b,c(z) satisfies the inequalities ∣(1 + (zu″p(z)/u′p(z)))2 − 1∣ &lt; 1 or ∣((zup(z))′/up(z))2 − 1∣ &lt; 1. We also determine the condition on these parameters so that . Relations between the parameters μ and p are obtained such that the normalized Lommel function of first kind hμ,p(z) satisfies the subordination . Moreover, the properties of Alexander transform of the function hμ,p(z) are discussed.

scholarly journals Characterizations for certain subclasses of starlike and convex functions associated with Bessel functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1911-1917 ◽  
Author(s):  
Nak Cho ◽  
Hyo Lee ◽  
Rekha Srivastava
Keyword(s):  
Integral Operator ◽  
Bessel Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Bessel Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Starlike And Convex Functions ◽  
Generalized Bessel Function

In the present paper, we obtain some characterizations for a certain generalized Bessel function of the first kind to be in the subclasses SpT(?,?), UCT(?,?), PT(?) and CPT(?) of normalized analytic functions in the open unit disk U. Furthermore, we consider an integral operator related to the generalized Bessel Function which we have characterized here.

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

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