Some Symmetric Identities for the Multiple (p, q)-Hurwitz-Euler eta Function
Copyright policy )Some Symmetric Identities for the Multiple (p, q)-Hurwitz-Euler eta Function
The main purpose of this paper is to find some interesting symmetric identities for the ( p , q ) -Hurwitz-Euler eta function in a complex field. Firstly, we define the multiple ( p , q ) -Hurwitz-Euler eta function by generalizing the Carlitz’s form ( p , q ) -Euler numbers and polynomials. We find some formulas and properties involved in Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order. We find new symmetric identities for multiple ( p , q ) -Hurwitz-Euler eta functions. We also obtain symmetric identities for Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order by using symmetry about multiple ( p , q ) -Hurwitz-Euler eta functions. Finally, we study the distribution and symmetric properties of the zero of Carlitz’s form ( p , q ) -Euler numbers and polynomials with higher order.
- Hannam University Korea (Republic of)
- Dong-A University Korea (Republic of)
- Korea University Korea (Republic of)
\((p, q)\)-Euler numbers and polynomials of higher order, symmetry of the zero, Zeta functions and \(L\)-functions, Euler numbers and polynomials, \(q\)-Euler numbers and polynomials, higher order <i>q</i>-Euler numbers and polynomials, higher order \(q\)-Euler numbers and polynomials, multiple Hurwitz-Euler eta function, symmetric identities, <i>q</i>-Euler numbers and polynomials, Hurwitz-Euler eta function, (<i>p</i>, <i>q</i>)-Euler numbers and polynomials of higher order, Bernoulli and Euler numbers and polynomials, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
\((p, q)\)-Euler numbers and polynomials of higher order, symmetry of the zero, Zeta functions and \(L\)-functions, Euler numbers and polynomials, \(q\)-Euler numbers and polynomials, higher order <i>q</i>-Euler numbers and polynomials, higher order \(q\)-Euler numbers and polynomials, multiple Hurwitz-Euler eta function, symmetric identities, <i>q</i>-Euler numbers and polynomials, Hurwitz-Euler eta function, (<i>p</i>, <i>q</i>)-Euler numbers and polynomials of higher order, Bernoulli and Euler numbers and polynomials, Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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