• Journal of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.391-410
• /
• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• Korean Journal of Mathematics
• /
• v.26 no.3
• /
• pp.405-424
• /
• 2018

In this paper we study some comparative growth properties of composite entire functions on the basis of relative (p, q)-th order and relative (p, q)-th lower order of entire function with respect to another entire function where p and q are any two positive integers.

• Journal of applied mathematics & informatics
• /
• v.37 no.1_2
• /
• pp.97-103
• /
• 2019

In this paper, we give some interesting symmetric identities of the (p, q)-Hurwitz zeta function. We also give some new interesting properties, explicit formulas, a connection with (p, q)-Bernoulli numbers and polynomials.

• Kyungpook Mathematical Journal
• /
• v.54 no.1
• /
• pp.131-141
• /
• 2014

In the present paper, we introduce the new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give some interesting identities. Finally, by applying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation for this polynomials at negative integers.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.915-929
• /
• 2007

The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.599-610
• /
• 2018

We aim to present some formulas for Saigo hypergeometric fractional integral and differential operators involving (p, q)-extended Bessel function $J_{{\nu},p,q}(z)$, which are expressed in terms of Hadamard product of the (p, q)-extended Gauss hypergeometric function and the Fox-Wright function $_p{\Psi}_q(z)$. A number of interesting special cases of our main results are also considered. Further, it is emphasized that the results presented here, which are seemingly complicated series, can reveal their involved properties via those of the two known functions in their respective Hadamard product.

• ETRI Journal
• /
• v.32 no.1
• /
• pp.145-147
• /
• 2010

In this letter, we present a new approximation for the twodimensional (2-D) Gaussian Q-function. The result is represented by only the one-dimensional (1-D) Gaussian Q-function. Unlike the previous 1-D Gaussian-type approximation, the presented approximation can be applied to compute the 2-D Gaussian Q-function with large correlations.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.873-882
• /
• 2022

In this paper, we construct the multiple (h, p, q)-Hurwitz-Euler eta function by generalizing the multiple Hurwitz-Euler eta function. We get some explicit formulas and properties of the higher-order (h, p, q)-Euler numbers and polynomials.

• Journal of applied mathematics & informatics
• /
• v.36 no.5_6
• /
• pp.555-565
• /
• 2018

The main subject of this paper is to introduce the (p, q)-Euler polynomials and obtain several interesting symmetric properties of the modified (p, q)-Hurwitz Euler Zeta function with regard to (p, q) Euler polynomials. In order to get symmetric properties, we introduce the new (p, q)-analogue of Euler polynomials $E_{n,p,q}(x)$ and numbers $E_{n,p,q}$.

• The Pure and Applied Mathematics
• /
• v.29 no.1
• /
• pp.69-91
• /
• 2022

In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p, q, t)L-th order, relative (p, q, t)L-th type and relative (p, q, t)L-th weak type and that of Wronskian generated by one of the factors.