• Title/Summary/Keyword: Special functions

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Development and Application of Visiting Physical-Computing Experience in an Education Program

  • Lee, Eun-Sang
    • Journal of the Korea Society of Computer and Information
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    • v.27 no.9
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    • pp.279-286
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    • 2022
  • The purpose of this study is to present a case of the development and application of a one-time special lecture program that requires the use of computers in frontline elementary and secondary schools. For this purpose, the researcher developed an Arduino-based special lecture program that works as a teaching tool to help with the functions of a student PC with a Raspberry Pi. This special lecture program was applied at three elementary and middle schools near K-University, and then the program was evaluated. The results of this study are as follows. First, the researcher developed a teaching aid for PC functions to be used in special lectures. Second, teaching and learning materials for visiting special lecture education programs using Arduino were developed. Third, in the special lecture, a teaching-learning method was used to guide a small number of students individually. Fourth, the special lecture program resulted in high satisfaction. The results of this study can be a useful reference for teachers who plan one-time special lecture programs requiring computers or for those who want to apply physical computing-related devices in an educational field.

On a New Theorem Involving the $\bar{H}$-function and a General Class of Polynomials

  • SHARMA, R.P.
    • Kyungpook Mathematical Journal
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    • v.43 no.4
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    • pp.489-494
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    • 2003
  • In this paper, we first establish an interesting theorem involving the $\bar{H}$-function introduced by Inayat-Hussain ([7], [8]). The convergence and existence condition, basic properties of this function were given by Buschman and Srivastava ([2]). Next, we obtain certain new integrals and an expansion formula by the application of our theorem. On account of the most general nature of the functions involved herein, our main findings are capable of yielding a large number of new, interesting and useful integrals, expansion formulae involving simple special functions and polynomials as their special cases. A known special case of our main theorem in also given ([11]).

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ON DOUBLE INFINITE SERIES INVOLVING THE H-FUNCTION OF TWO VARIABLES

  • Handa, S.
    • Kyungpook Mathematical Journal
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    • v.18 no.2
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    • pp.257-262
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    • 1978
  • In this paper, we obtain two new double infinite series for the H-function of two variables, by which we also obtain a single infinite series involving the H-function of two variable3. On account of the most general nature of the H-functin of two variables, a number of related double infinite series for simpler functions follow as special cases of our results. As an illustration, we obtain here from one of our main series, the corresponding series for $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function and Fox's H-function. A number of other series involving a very large, spectrum of special functions also follow as special cases of our main series but, we are not recording them here for want of space.

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The Incomplete Lauricella Functions of Several Variables and Associated Properties and Formulas

  • Choi, Junesang;Parmar, Rakesh K.;Srivastava, H.M.
    • Kyungpook Mathematical Journal
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    • v.58 no.1
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    • pp.19-35
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    • 2018
  • Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

A FURTHER GENERALIZATION OF APOSTOL-BERNOULLI POLYNOMIALS AND RELATED POLYNOMIALS

  • Tremblay, R.;Gaboury, S.;Fugere, J.
    • Honam Mathematical Journal
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    • v.34 no.3
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    • pp.311-326
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    • 2012
  • The purpose of this paper is to introduce and investigate two new classes of generalized Bernoulli and Apostol-Bernoulli polynomials based on the definition given recently by the authors [29]. In particular, we obtain a new addition formula for the new class of the generalized Bernoulli polynomials. We also give an extension and some analogues of the Srivastava-Pint$\acute{e}$r addition theorem [28] for both classes. Finally, by making use of the new adition formula, we exhibit several interesting relationships between generalized Bernoulli polynomials and other polynomials or special functions.

A design of transcendental function arithmetic unit for lighting operation of mobile 3D graphic processor (모바일 3차원 그래픽 프로세서의 조명처리 연산을 위한 초월함수 연산기 구현)

  • Lee, Sang-Hun;Lee, Chan-Ho
    • Proceedings of the IEEK Conference
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    • 2005.11a
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    • pp.715-718
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    • 2005
  • Mobile devices is getting to include more functions according to the demand of digital convergence. Applications based on 3D graphic calculation such as 3D games and navigation are one of the functions. 3D graphic calculation requires heavy calculation. Therefore, we need dedicated 3D graphic hardware unit with high performance. 3D graphic calculation needs a lot of complicated floating-point arithmetic operation. However, most of current mobile 3D graphics processors do not have efficient architecture for mobile devices because they are based on those for conventional computer systems. In this paper, we propose arithmetic units for special functions of lighting operation of 3D graphics. Transcendental arithmetic units are designed using approximation of logarithm function. Special function units for lighting operation such as reciprocal, square root, reciprocal of square root, and power can be obtained. The proposed arithmetic unit has lower error rate and smaller silicon area than conventional arithmetic architecture.

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On Certain Integral Transforms Involving Hypergeometric Functions and Struve Function

  • Singhal, Vijay Kumar;Mukherjee, Rohit
    • Kyungpook Mathematical Journal
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    • v.56 no.4
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    • pp.1169-1177
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    • 2016
  • This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings.

CERTAIN GENERALIZED AND MIXED TYPE GENERATING RELATIONS: AN OPERATIONAL APPROACH

  • Khan, Rehana;Kumar, Naresh;Qamar, Ruma
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.473-484
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    • 2018
  • In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

INCLUSION AND NEIGHBORHOOD PROPERTIES OF CERTAIN SUBCLASSES OF p-VALENT ANALYTIC FUNCTIONS OF COMPLEX ORDER INVOLVING A LINEAR OPERATOR

  • Sahoo, Ashok Kumar;Patel, Jagannath
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1625-1647
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    • 2014
  • By making use of the familiar concept of neighborhoods of analytic functions, we prove several inclusion relationships associated with the (n, ${\delta}$)-neighborhoods of certain subclasses of p-valent analytic functions of complex order with missing coefficients, which are introduced here by means of the Saitoh operator. Special cases of some of the results obtained here are shown to yield known results.

ON FOUR NEW MOCK THETA FUNCTIONS

  • Hu, QiuXia
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.345-354
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    • 2020
  • In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of 2𝜓2 series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.