The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and those of the second author for Euler’s constant γ and its alternating analog ln(4/π), and on the other hand the infinite products of the first author for e, and of the second author for π and e . We obtain new double integral and infinite product representations of man...

In this paper, we give a natural construction of mixed Tate motives whose periods are a class of iterated integrals which include the multiple polylogarithm functions. Given such an iterated integral, we construct two divisors A and B in the moduli spacesM0,n of n-pointed stable curves of genus 0, and prove that the cohomology of the pair (M0,n−A,B−B∩A) is a framed mixed Tate motive whose perio...

Some fundamental inequalities for Lerch transcendent function with positive terms by utilising certain classical results due to Hölder, Čebyšev, Grüss and others, are established. particular cases of interest Polylogarithm function, Hurwitz zeta Legendre chi also given.

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4, 7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle...

The specializations of the motivic elliptic polylogarithm on the universal elliptic curve to the modular curve are referred to as Eisenstein classes. In this paper, we prove that the syntomic realizations of the Eisenstein classes restricted to the ordinary locus of the modular curve may be expressed using p-adic Eisenstein-Kronecker series, which are p-adic modular forms defined using the two-...

For any positive integer N let μN be the group of the N th roots of unity. In this note we shall study the Q-linear relations among the values of multiple polylogarithms evaluated at μN . We show that the standard relations considered by Racinet do not provide all the possible relations in the following cases: (i) level N = 4, weight w = 3 or 4, and (ii) w = 2, 7 <N < 50, and N is a power of 2 ...