Related papers: Generating functions of multiple $t$-star values

In this paper, we establish some expressions of series involving harmonic numbers and Stirling numbers of the first kind in terms of multiple zeta values, and present some new relationships between multiple zeta values and multiple zeta…

We give an explicit representation for the sums of multiple zeta-star values of fixed weight and height in terms of Riemann zeta values.

We prove that the sum of multiple zeta-star values over all indices inserted two 2's into the string $(\underbrace{3,1, ..., 3,1}_{2n})$ is evaluated to a rational multiple of powers of $\pi^2$. We also establish certain conjectures on…

In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,...,2. Our identities give analogues of Zagier's evaluation of \zeta(2,...,2,3,2,..., 2) and examples of a…

We consider multi-polylogarithm functions which are slightly different from the ordinary ones. These functions have two integral representations and an order structure similar to those of multiple zeta star values. We also give a necessary…

For a simple graph we introduce notions of the double star sequence, the double star frequently sequence and prove that these sequences are inverses of each other. As a consequence, we express the general second Zagreb index in terms of the…

We evaluate, by elementary means, a new family of Ap\'ery-like series involving multiple $t$-harmonic star sums of even weight. Using trigonometric expansions, inverse tangent integrals, and binomial recurrences, we obtain explicit…

We define polynomials of one variable t whose values at t=0 and 1 are the multiple zeta values and the multiple zeta-star values, respectively. We give an application to the two-one conjecture of Ohno-Zudilin, and also prove the cyclic sum…

It is demonstrated how an explicit expression of the (partial) sum of Tetranacci numbers can be found and proved using generating functions and the Hadamard product. We also provide a Binet-type formula for generalized Fibonacci numbers, by…

In this paper we establish several recurrence relations about Euler-Ap\'ery type multiple zeta star values and a parametric variant of it by using the method of iterated integrals. Then using the formulas obtained, we find the explicit…

Discussion of the designation of multiple-star components leads to a conclusion that, apart from components, we need to designate systems and centers-of-mass. The hierarchy is coded then by simple links to parent. This system is adopted in…

In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of $\pi^2$.

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

In this paper we define a continuous version of multiple zeta functions. They can be analytically continued to meromorphic functions on $\mathbb{C}^r$ with only simple poles at some special hyperplanes. The evaluations of these functions at…

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

In this work we show a technique that allows for the musical interpretation of the brightness variations of stars. This method allows composers a lot of freedom to incorporate their own ideas into the score, based on the melodic line…

We construct the generating function for products of inverse central binomial coefficients with harmonic numbers.

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…

The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…

The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…