• 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.

• 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.

• 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.

• 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.

• 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 e^λt for e^t 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.

• 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.

• Journal of applied mathematics & informatics
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• v.41 no.2
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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 F_p,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.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.47-54
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• 1994

We present a generating function and three semi-orthogonal relations for a class of hypergeometric functions. We employ semi-orthogonal relations to generate a theory concerning finite series expansions involving our hypergeometric functions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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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.

• Korean Journal of Mathematics
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• v.27 no.2
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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.