• 제목/요약/키워드: the Bessel functions

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DIFFERENTIAL SUBORDINATIONS AND SUPERORDINATIONS FOR GENERALIZED BESSEL FUNCTIONS

  • Al-Kharsani, Huda A.;Baricz, Arpad;Nisar, Kottakkaran S.
    • 대한수학회보
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    • 제53권1호
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    • pp.127-138
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    • 2016
  • Differential subordination and superordination preserving properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.

BOUNDS FOR RADII OF CONVEXITY OF SOME q-BESSEL FUNCTIONS

  • Aktas, Ibrahim;Orhan, Halit
    • 대한수학회보
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    • 제57권2호
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    • pp.355-369
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    • 2020
  • In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.

Certain Geometric Properties of an Integral Operator Involving Bessel Functions

  • Selvakumaran, Kuppathai Appasamy;Szasz, Robert
    • Kyungpook Mathematical Journal
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    • 제58권3호
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    • pp.507-517
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    • 2018
  • In this article, we introduce a new integral operator involving normalized Bessel functions of the first kind and we obtain a set of sufficient conditions for univalence. Our results contain some interesting corollaries as special cases. Further, as particular cases, we improve some of the univalence conditions proved in [2].

APPARENT INTEGRALS MOUNTED WITH THE BESSEL-STRUVE KERNEL FUNCTION

  • Khan, N.U.;Khan, S.W.
    • 호남수학학술지
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    • 제41권1호
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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.

EXTENSIONS OF MULTIPLE LAURICELLA AND HUMBERT'S CONFLUENT HYPERGEOMETRIC FUNCTIONS THROUGH A HIGHLY GENERALIZED POCHHAMMER SYMBOL AND THEIR RELATED PROPERTIES

  • Ritu Agarwal;Junesang Choi;Naveen Kumar;Rakesh K. Parmar
    • 대한수학회보
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    • 제60권3호
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    • pp.575-591
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    • 2023
  • Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F(n)A and the Humbert's confluent hypergeometric function Ψ(n) of n variables with, as their respective particular cases, the second Appell hypergeometric function F2 and the generalized Humbert's confluent hypergeometric functions Ψ2 and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

FUNCTIONAL RELATIONS INVOLVING SRIVASTAVA'S HYPERGEOMETRIC FUNCTIONS HB AND F(3)

  • Choi, Junesang;Hasanov, Anvar;Turaev, Mamasali
    • 충청수학회지
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    • 제24권2호
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    • pp.187-204
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    • 2011
  • B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

FORMULAS AND RELATIONS FOR BERNOULLI-TYPE NUMBERS AND POLYNOMIALS DERIVE FROM BESSEL FUNCTION

  • Selin Selen Ozbek Simsek;Yilmaz Simsek
    • 대한수학회논문집
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    • 제38권4호
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    • pp.1175-1189
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    • 2023
  • The main purpose of this paper is to give some new identities and properties related to Bernoulli type numbers and polynomials associated with the Bessel function of the first kind. We give symmetric properties of the Bernoulli type numbers and polynomials. Moreover, using generating functions and the Faà di Bruno's formula, we derive some new formulas and relations related to not only these polynomials, but also the Bernoulli numbers and polynomials and the Euler numbers and polynomials.

A FAMILY OF SERIES AND INTEGRALS INVOLVING WHITTAKER, BESSEL FUNCTIONS, AND THEIR PRODUCTS DERIVABLE FROM THE REPRESENTATION OF THE GROUP SO(2, 1)

  • Choi, Junesang;Shilin, I.A.
    • 대한수학회논문집
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    • 제32권4호
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    • pp.999-1008
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    • 2017
  • By mainly using certain properties arising from the semisimple Lie group SO(2, 1), we aim to show how a family of some interesting formulas for bilateral series and integrals involving Whittaker, Bessel functions, and their product can be obtained.

A NEW SUBCLASS OF MEROMORPHIC FUNCTIONS ASSOCIATED WITH BESSEL FUNCTIONS

  • SUJATHA;B. VENKATESWARLU;P. THIRUPATHI REDDY;S. SRIDEVI
    • Journal of applied mathematics & informatics
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    • 제41권5호
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    • pp.907-921
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    • 2023
  • In this article, we are presenting and examining a subclass of Meromorphic univalent functions as stated by the Bessel function. We get disparities in terms of coefficients, properties of distortion, closure theorems, Hadamard product. Finally, for the class Σ*(℘, ℓ, ℏ, τ, c), we obtain integral transformations.