• Title, Summary, Keyword: 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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    • v.5 no.2
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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.

Some Generating Relations of Extended Mittag-Leffler Functions

  • Khan, Nabiullah;Ghayasuddin, Mohd;Shadab, Mohd
    • Kyungpook Mathematical Journal
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    • v.59 no.2
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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.

GENERATING FUNCTIONS FOR THE EXTENDED WRIGHT TYPE HYPERGEOMETRIC FUNCTION

  • Jana, Ranjan Kumar;Maheshwari, Bhumika;Shukla, Ajay Kumar
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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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.

GENERALIZED 'USEFUL' INFORMATION GENERATING FUNCTIONS

  • Hooda, D.S.;Sharma, D.K.
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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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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Performance Analysis of Generating Function Approach for Optimal Reconfiguration of Formation Flying

  • Lee, Kwangwon;Park, Chandeok;Park, Sang-Young
    • Journal of Astronomy and Space Sciences
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    • v.30 no.1
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    • pp.17-24
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    • 2013
  • The use of generating functions for solving optimal rendezvous problems has an advantage in the sense that it does not require one to guess and iterate the initial costate. This paper presents how to apply generating functions to analyze spacecraft optimal reconfiguration between projected circular orbits. The series-based solution obtained by using generating functions demonstrates excellent convergence and approximation to the nonlinear reference solution obtained from a numerical shooting method. These favorable properties are expected to hold for analyzing optimal formation reconfiguration under perturbations and non-circular reference orbits.

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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    • v.38 no.3_4
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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.

EVALUATIONS OF $\zeta(2n)$

  • Choi, June-Sang
    • East Asian mathematical journal
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    • v.16 no.2
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    • pp.233-237
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    • 2000
  • Since the time of Euler, there have been many proofs giving the value of $\zeta(2n)$. We also give an evaluation of $\zeta(2n)$ by analyzing the generating function of Bernoulli numbers.

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ENUMERATION OF GRAPHS WITH GIVEN WEIGHTED NUMBER OF CONNECTED COMPONENTS

  • Song, Joungmin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.6
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    • pp.1873-1882
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    • 2017
  • We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of q-partite graphs of given order, size and number of connected components.