2 citations · 3 across the 10 of their papers we have counts for
14 papers
Values of zeta-one functions at positive even integers
Masato Kobayashi, Shunji Sasaki
Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of as an analogy of the Riemann zeta function. Then we comput…
Integral representations for local dilogarithm and trilogarithm functions
Masato Kobayashi
We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Ca…
Matrix representation of meet-irreducible discrete copulas
Masato Kobayashi
Following Aguiló-Suñer-Torrens (2008), Kolesárová-Mesiar-Mordelová-Sempi (2006) and Mayor-Suñer-Torrens (2005), we continue to develop a theory of matrix representation for discret…
New relations on zeta and functions
Masato Kobayashi
We prove new relations on zeta function at even arguments and Dirichlet function at odd. The key idea is to make use of the Taylor series and partial fraction decomposition of…
Möbius functions of higher rank and Dirichlet series
Masato Kobayashi
We introduce Möbius functions of higher rank, a new class of arithmetic functions so that the classical Möbius function is of rank 2. With this idea, we evaluate Dirichlet series o…
Integral representations for with the inverse sine function
Masato Kobayashi
We show four new integral representations for as a reformulation of Ewell (1990) and Yue-Williams (1993) with the inverse sine function and Wallis integral. As a consequence…