• Title/Summary/Keyword: Wright Hypergeometric Function and Integrals

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APPARENT INTEGRALS MOUNTED WITH THE BESSEL-STRUVE KERNEL FUNCTION

  • Khan, N.U.;Khan, S.W.
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.163-174
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    • 2019
  • The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.

A NEW CLASS OF EULER TYPE INTEGRAL OPERATORS INVOLVING MULTIINDEX MITTAG-LEFFLER FUNCTION

  • Khan, Nabiullah;Ghayasuddin, Mohd.;Shadab, Mohd
    • Honam Mathematical Journal
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    • v.40 no.4
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    • pp.691-700
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    • 2018
  • The main object of the present research paper is to establish two (potentially) useful Euler type integrals involving multiindex Mittag-Leffler functions, which are expressed in terms of Wright hypergeometric functions. Some deductions of the main results are also indicated.

SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS

  • KHAN, N.U.;USMAN, T.;GHAYASUDDIN, M.
    • Journal of applied mathematics & informatics
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    • v.34 no.3_4
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    • pp.249-255
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    • 2016
  • The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.

CERTAIN UNIFIED INTEGRALS INVOLVING A PRODUCT OF BESSEL FUNCTIONS OF THE FIRST KIND

  • Choi, Junesang;Agarwal, Praveen
    • Honam Mathematical Journal
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    • v.35 no.4
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    • pp.667-677
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    • 2013
  • A remarkably large number of integrals involving a product of certain combinations of Bessel functions of several kinds as well as Bessel functions, themselves, have been investigated by many authors. Motivated the works of both Garg and Mittal and Ali, very recently, Choi and Agarwal gave two interesting unified integrals involving the Bessel function of the first kind $J_{\nu}(z)$. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present two generalized integral formulas involving a product of Bessel functions of the first kind, which are expressed in terms of the generalized Lauricella series due to Srivastava and Daoust. Some interesting special cases and (potential) usefulness of our main results are also considered and remarked, respectively.

CERTAIN INTEGRATION FORMULAE FOR THE GENERALIZED k-BESSEL FUNCTIONS AND DELEURE HYPER-BESSEL FUNCTION

  • Kim, Yongsup
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.523-532
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    • 2019
  • Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi et al. [2, 3]. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized k-Bessel functions. Also, we consider some integral formulas of the (p, q)-extended Bessel functions $J_{{\nu},p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of (p, q)-extended generalized hypergeometric functions, and the generalized Wright hypergeometric functions, respectively.

CERTAIN UNIFIED INTEGRALS INVOLVING PRODUCT OF GENERALIZED k-BESSEL FUNCTION AND GENERAL CLASS OF POLYNOMIALS

  • Menaria, N.;Parmar, R.K.;Purohit, S.D.;Nisar, K.S.
    • Honam Mathematical Journal
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    • v.39 no.3
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    • pp.349-361
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    • 2017
  • By means of the Oberhettinger integral, certain generalized integral formulae involving product of generalized k-Bessel function $w^{{\gamma},{\alpha}}_{k,v,b,c}(z)$ and general class of polynomials $S^m_n[x]$ are derived, the results of which are expressed in terms of the generalized Wright hypergeometric functions. Several new results are also obtained from the integrals presented in this paper.

Generalizations of Ramanujan's Integral Associated with Infinite Fourier Cosine Transforms in Terms of Hypergeometric Functions and its Applications

  • Qureshi, Mohammad Idris;Dar, Showkat Ahmad
    • Kyungpook Mathematical Journal
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    • v.60 no.4
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    • pp.781-795
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    • 2020
  • In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

A STUDY OF NEW CLASS OF INTEGRALS ASSOCIATED WITH GENERALIZED STRUVE FUNCTION AND POLYNOMIALS

  • Haq, Sirazul;Khan, Abdul Hakim;Nisar, Kottakkaran Sooppy
    • Communications of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.169-183
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    • 2019
  • The main aim of this paper is to establish a new class of integrals involving the generalized Galu$Galu{\grave{e}}$-type Struve function with the different type of polynomials such as Jacobi, Legendre, and Hermite. Also, we derive the integral formula involving Legendre, Wright generalized Bessel and generalized Hypergeometric functions. The results obtained here are general in nature and can deduce many known and new integral formulas involving the various type of polynomials.

FINITE INTEGRALS ASSOCIATED WITH THE PRODUCT OF ORTHOGONAL POLYNOMIALS AND WRIGHT FUNCTION

  • Khan, Nabiullah;Khan, Mohammad Iqbal;Khan, Owais
    • Honam Mathematical Journal
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    • v.43 no.4
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    • pp.597-612
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    • 2021
  • Several useful and interesting extensions of the various special functions have been introduced by many authors during the last few decades. Various integral formulas associated with Wright function have been studied and a noteworthy amount of work have found in literature. The principal object of the present paper is to evaluate finite integral formulas containing the product of orthogonal polynomials with generalized Wright function. These integral formulas are expressed in terms of Srivastava and Daoust function. Some interesting particular cases are obtained from the main results by specialising the suitable values of the parameters involved.

CERTAIN FRACTIONAL INTEGRALS AND IMAGE FORMULAS OF GENERALIZED k-BESSEL FUNCTION

  • Agarwal, Praveen;Chand, Mehar;Choi, Junesang;Singh, Gurmej
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.423-436
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    • 2018
  • We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.