17 citations · 60 across the 14 of their papers we have counts for
19 papers
On values of finite multiple harmonic -series at roots of unity
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
We mainly answer two open questions about finite multiple harmonic -series on 3-2-1 indices at roots of unity, posed recently by H. Bachmann, Y. Takeyama, and K. Tasaka. Two con…
Multiple zeta star values on 3-2-1 indices
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In 2008, Muneta found explicit evaluation of the multiple zeta star value , and in 2013, Yamamoto proved a sum formula for multiple zeta star values on 3-2-1 i…
Generating functions for multiple zeta star values
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler su…
Multiple harmonic sums and multiple harmonic star sums are (nearly) never integers
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
It is well known that the harmonic sum is never an integer for . In 1946, Erdős and Niven proved that the nested multiple harmonic sum $H_n(\{…
Jacobi polynomials and congruences involving some higher-order Catalan numbers and binomial coefficients
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In this paper, we study congruences on sums of products of binomial coefficients that can be proved by using properties of the Jacobi polynomials. We give special attention to poly…
Some -congruences for homogeneous and quasi-homogeneous multiple -harmonic sums
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
We show some new Wolstenholme type -congruences for some classes of multiple -harmonic sums of arbitrary depth with strings of indices composed of ones, twos and threes. Most…
On -Analogs of Some Families of Multiple Harmonic Sum and Multiple Zeta Star Value Identities
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Jianqiang Zhao
In recent years, there has been intensive research on the -linear relations between multiple zeta (star) values. In this paper, we prove many families of identities in…
New properties of multiple harmonic sums modulo and -analogues of Leshchiner's series
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
In this paper we present some new identities of hypergeometric type for multiple harmonic sums whose indices are the sequences and prov…
Congruences concerning Jacobi polynomials and Apéry-like formulae
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso
Let be a prime. We prove congruences modulo for sums of the general form and $\sum_{k=1}^{(p-1)/2}\binom{2k}{k}t…
Congruences arising from Apéry-type series for zeta values
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
Recently, R. Tauraso established finite -analogues of famous Apéry series for and In this paper, we present several congruences for finite central binomial sums a…
Bivariate identities for values of the Hurwitz zeta function and supercongruences
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley…
Rational approximations to values of Bell polynomials at points involving Euler's constant and zeta values
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In this paper, we present new explicit simultaneous rational approximations converging sub-exponentially to the values of Bell polynomials at the points of the form $(γ, 1! (2a+1)ζ…
On a continued fraction expansion for Euler's constant
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
Recently, A. I. Aptekarev and his collaborators found a sequence of rational approximations to Euler's constant defined by a third-order homogeneous linear recurrence. In this…
Rational approximations for the quotient of gamma values
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recen…
Rational approximations for values of the digamma function and a denominators conjecture
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
In 2007, A.I.Aptekarev and his collaborators discovered a sequence of rational approximations to Euler's constant defined by a linear recurrence. In this paper, we generalize t…
Vacca-type series for values of the generalized-Euler-constant function and its derivative
Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood
We generalize well-known Catalan-type integrals for Euler's constant to values of the generalized-Euler-constant function and its derivatives. Using generating functions appeared i…
Simultaneous generation for zeta values by the Markov-WZ method
Kh. Hessami Pilehrood, T. Hessami Pilehrood
By application of the Markov-WZ method, we prove a more general form of a bivariate generating function identity containing, as particular cases, Koecher's and Almkvist-Granville's…
Generating function identities for via the WZ method
Kh. Hessami Pilehrood, T. Hessami Pilehrood
Using the WZ method we present simpler proofs of Koecher's, Leshchiner's and Bailey-Borwein-Bradley's identities for generating functions of the sequences $\{ζ(2n+2)\}_{n\ge 0}, \{…
Approximations to Euler's constant
Kh. Hessami Pilehrood, T. Hessami Pilehrood
We study a problem of finding good approximations to Euler's constant where by linear forms in logarithms and har…