• 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.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1277-1292
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• 2009

This paper is an attempt to stress the usefulness of the multivariable special functions. In this paper, we derive generating relations involving 3-variable 2-parameter Tricomi functions by using Lie-algebraic techniques. Further we derive certain new and known generating relations involving other forms of Tricomi and Bessel functions as applications.

• 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.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.429-438
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• 2015

In this paper, we discuss how the operational calculus can be exploited to the theory of mixed generating functions. We use operational methods associated with multi-variable Hermite polynomials, Laguerre polynomials and Bessels functions to drive identities useful in electromagnetism, fluid mechanics etc. Certain special cases giving bilateral generating relations related to these special functions are also discussed.

• 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 the Korean Mathematical Society
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• v.50 no.5
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.35-44
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• 2017

The present paper aims at harnessing the technique of Lie Algebra and operational methods to derive and interpret generating relations for the three-variable Hermite Polynomials $H_n$(x, y, z) introduced recently in [2]. Certain generating relations for the polynomials related to $H_n$(x, y, z) are also obtained as special cases.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.731-752
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• 2020

We introduce the p-deformation of generalized Humbert polynomials. For these polynomials, we derive the differential equation, generating function relations, Fibonacci-type representations, and recurrence relations and state the companion matrix. These properties are illustrated for certain polynomials belonging to p-deformed generalized Humbert polynomials.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.265-284
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• 2019

The main purpose of this paper is to investigate the q-Apostol type Frobenius-Euler numbers and polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive q-integers. By using infinite series representation for q-Apostol type Frobenius-Euler numbers and polynomials including their interpolation functions, we not only give some identities and relations for these numbers and polynomials, but also define generating functions for new numbers and polynomials. Further we give remarks and observations on generating functions for these new numbers and polynomials. By using these generating functions, we derive recurrence relations and finite sums related to these numbers and polynomials. Moreover, by applying higher-order derivative to these generating functions, we derive some new formulas including the Hurwitz-Lerch zeta function, the Apostol-Bernoulli numbers and the Apostol-Euler numbers. Finally, for an application of the generating functions, we derive a multiplication formula, which is very important property in the theories of normalized polynomials and Dedekind type sums.

• 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.