Approximations to q-logarithms and q-dilogarithms, with applications to q-zeta values
نویسندگان
چکیده
منابع مشابه
Multiple q-zeta values
We introduce a q-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple q-zeta values satisfy a q-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the series representation of ordinary multiple zeta values. Additionally, multiple q-zeta values can be viewed as special values of the multiple q-polylogarithm, which ad...
متن کاملSUM OF MULTIPLE q-ZETA VALUES
The generating function of the sums of multiple q-zeta values with fixed weights, depths and 1-heights, 2-heights, . . . , r-heights is represented in terms of specializations of basic hypergeometric functions.
متن کاملDIOPHANTINE PROBLEMS FOR q-ZETA VALUES 1
hold. The above defined q-zeta values (1) present several new interesting problems in the theory of diophantine approximations and transcendental numbers; these problems are extensions of the corresponding problems for ordinary zeta values and we state some of them in Section 3 of this note. Our nearest aim is to demonstrate how some recent contributions to the arithmetic study of the numbers ζ...
متن کاملRenormalization of Multiple q-Zeta Values
Abstract. In this paper we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq(s1, . . . , sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang [12] on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process pr...
متن کاملq-EULER NUMBERS AND POLYNOMIALS ASSOCIATED WITH p-ADIC q-INTEGRALS AND BASIC q-ZETA FUNCTION
The purpose of this paper is to introduce the some interesting properties of q-Euler numbers and polynomials, cf. [1, 2, 5]. Finally, we will consider the “ sums of products of q-Euler polynomials”.
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2006
ISSN: 1072-3374,1573-8795
DOI: 10.1007/s10958-006-0263-y