Related papers: Explicit Formula for Witten-Kontsevich Tau-Functio…

We study Ramanujan's cubic continued fraction and explicit evaluations of theta-functions

In this paper, we give a simple proof of the functional relation for the Lerch type Tornheim double zeta function. By using it, we obtain simple proofs of some explicit evaluation formulas for double $L$-values.

We present an integral representation formula for a Dirichlet series whose coefficients are the values of the Liouville's arithmetic function.

In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in computation of higher-dimensional…

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla-Selberg series formula, for which an alternative proof is thereby…

In this article, we present relations for the Euler totient function $\varphi(n)$ and the number of divisors $\tau(n)$ in terms of finite sums of integer parts of rational numbers or greatest common divisors of pairs of integers. Some of…

The main aim of this paper is to find the estimation for Vilenkin-Fourier coefficients.

In the note, the author discovers an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

With the modified Riemann-Liouville fractional derivative, a fractional Tu formula is presented to investigate generalized Hamilton structure of fractional soliton equations. The obtained results can be reduced to the classical Hamilton…

In our previous works, a relationship between Hermite's two approximation problems and Schlesinger transformations of linear differential equations has been clarified. In this paper, we study tau-functions associated with holonomic…

We consider two approaches for obtain of the generalized Ito-Wentzell formula: the first way uses the generalized Ito's formula; the second one is based on a concept of kernel functions for integral invariants.

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

In this paper we obtain large $z$ asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlev\'e II differential equation. Using the fact that these tau functions can be written…

Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.

Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…

A computation of the Isgur-Wise universal form factor using a lattice implementation of the heavy quark effective theory is described, and the results of a lattice simulation are presented.

The main goal of this paper is to provide a group theoretical generalization of the well-known Euler's totient function. This determines an interesting class of finite groups.

We present a new variant of the Faa di Bruno formula with a simpler summation order.

The Riemann zeta function on the critical line can be computed using a straightforward application of the Riemann-Siegel formula, Sch\"onhage's method, or Heath-Brown's method. The complexities of these methods have exponents 1/2, 3/8…

We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities…