• 제목/요약/키워드: Generating function

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Generating functions for t-norms

  • Kim, Yong-Chan;Ko, Jung-Mi
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제5권2호
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    • pp.140-144
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    • 2005
  • We investigate the P-generating functions, L-generating functions, and A-generating function, respectively induced by product t-norms, Lukasiewicz t-norms and additive semi-groups. Furthermore, we investigate the relations among them.

GENERATING FUNCTIONS FOR THE EXTENDED WRIGHT TYPE HYPERGEOMETRIC FUNCTION

  • Jana, Ranjan Kumar;Maheshwari, Bhumika;Shukla, Ajay Kumar
    • 대한수학회논문집
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    • 제32권1호
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    • pp.75-84
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    • 2017
  • In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.

Some Generating Relations of Extended Mittag-Leffler Functions

  • Khan, Nabiullah;Ghayasuddin, Mohd;Shadab, Mohd
    • Kyungpook Mathematical Journal
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    • 제59권2호
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    • pp.325-333
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    • 2019
  • Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Leffler-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Leffler function. Also we present some special cases of our main result.

GENERALIZED 'USEFUL' INFORMATION GENERATING FUNCTIONS

  • Hooda, D.S.;Sharma, D.K.
    • Journal of applied mathematics & informatics
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    • 제27권3_4호
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    • pp.591-601
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    • 2009
  • In the present paper, one new generalized 'useful' information generating function and two new relative 'useful' information generating functions have been defined with their particular and limiting cases. It is interesting to note that differentiations of these information generating functions at t=0 or t=1 give some known and unknown generalized measures of useful information and 'useful' relative information. The information generating functions facilitates to compute various measures and that has been illustrated by applying these information generating functions for Uniform, Geometric and Exponential probability distributions.

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A NOTE OF THE MODIFIED BERNOULLI POLYNOMIALS AND IT'S THE LOCATION OF THE ROOTS

  • LEE, Hui Young
    • Journal of applied mathematics & informatics
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    • 제38권3_4호
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    • pp.291-300
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    • 2020
  • This type of polynomial is a generating function that substitutes eλt for et in the denominator of the generating function for the Bernoulli polynomial, but polynomials by using this generating function has interesting properties involving the location of the roots. We define these generation functions and observe the properties of the generation functions.

GENERATING FUNCTIONS OF (p, q)-ANALOGUE OF ALEPH-FUNCTION SATISFYING TRUESDELL'S ASCENDING AND DESCENDING Fp,q-EQUATION

  • ALTAF A. BHAT;M. YOUNUS BHAT;H. MAQBOOL;D.K. JAIN
    • Journal of applied mathematics & informatics
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    • 제41권2호
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    • pp.373-386
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    • 2023
  • In this paper we have obtained various forms of (p, q)-analogue of Aleph-Function satisfying Truesdell's ascending and descending Fp,q-equation. These structures have been employed to arrive at certain generating functions for (p, q)-analogue of Aleph-Function. Some specific instances of these outcomes as far as (p, q)-analogue of I-function, H-function and G-functions have likewise been obtained.

OME PROPERTIES OF THE BERNOULLI NUMBERS OF THE SECOND KIND AND THEIR GENERATING FUNCTION

  • Qi, Feng;Zhao, Jiao-Lian
    • 대한수학회보
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    • 제55권6호
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    • pp.1909-1920
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    • 2018
  • In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

SIMPLIFYING COEFFICIENTS IN A FAMILY OF ORDINARY DIFFERENTIAL EQUATIONS RELATED TO THE GENERATING FUNCTION OF THE MITTAG-LEFFLER POLYNOMIALS

  • Qi, Feng
    • Korean Journal of Mathematics
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    • 제27권2호
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    • pp.417-423
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    • 2019
  • In the paper, by virtue of the $Fa{\grave{a}}$ di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag-Leffler polynomials.