Abstract We construct a new type of planar Euler flows with localized vorticity. Let $\kappa _i\not =0$ , $i=1,\ldots m$ be m arbitrarily fixed constants. For any given nondegenerate critical point $\mathbf {x}_0=(x_{0,1},\ldots ,x_{0,m})$ the Kirchhoff–Routh function defined on $\Omega ^m$ corresponding to $(\kappa _1,\ldots \kappa _m)$ we family stationary vortex sheets that have large vortic...

The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral ...

Recently, Choi et al. 2008 have studied the q-extensions of the Apostol-Bernoulli and the ApostolEuler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol’s type q-Euler numbers En,q,ξ and q-Euler polynomials En,q,ξ x . We obtain the generating functions of En,q,ξ and En,q,ξ x , respectively. We also have the distribution relation for Apostol’s type q-Eul...

Abstract. Recently, the q-Euler numbers and polynomials are constructed in [T. Kim, The modified q-Euler numbers and polynomials, Advanced Studies in Contemporary Mathematics, 16(2008), 161-170]. These q-Euler numbers and polynomials contain the interesting properties. In this paper we prove Von-Staudt Clausen’s type theorem related to the q-Euler numbers. That is, we prove that the q-Euler num...

(i) We present several limits associated with the Euler-Mascheroni constant. (ii) Let γ = 0.577215 . . . be the Euler-Mascheroni constant, and let Tn = ∑n k=1 1 k − ln ( n+ 1 2 + 1 24n ) and Pn = ∑n k=1 2 2k−1 − ln(4n). We determine the best possible constants α, β, a and b such that the inequalities 1 48(n+ α)3 ≤ γ − Tn < 1 48(n+ β)3 and 1 24(n+ a)2 ≤ Pn − γ < 1 24(n+ b)2 are valid for all int...

Let G be a finite group acting freely on a smooth projective scheme X over a locally compact field of characteristic 0. We show that the ε0-constants associated to symplectic representations V of G and the action of G on X may be determined from Pfaffian invariants associated to duality pairings on Hodge cohomology. We also use such Pfaffian invariants, along with equivariant Arakelov Euler cha...

This paper employs a contour integral method to derive and evaluate the infinite sum of Euler polynomial expressed in terms Hurwitz Zeta function. We provide formulae for several classes sums Riemann function fundamental mathematical constants, including Catalan’s constant. representation constant suggests it could be rational.

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...