3 citations · 6 across the 5 of their papers we have counts for
5 papers
The Generalization of Faulhaber's Formula to Sums of Arbitrary Complex Powers
Raphael Schumacher
In this paper we present a generalization of Faulhaber's formula to sums of arbitrary complex powers . These summation formulas for sums of the form $\sum_{k=1}^{\l…
Subconvexity for -Functions: The Key Identity via Integral Representations
Raphael Schumacher
We study the subconvexity problem for -functions in the t-aspect using integral representations by combining techniques employed by Michel-Venkatesh in their study o…
The Formulas for the Distribution of the 3-Smooth, 5-Smooth, 7-Smooth and all other Smooth Numbers
Raphael Schumacher
In this paper we present and prove rapidly convergent formulas for the distribution of the -smooth, -smooth, -smooth and all other smooth numbers. One of these formulas is…
Extension of Summation Formulas involving Stirling series
Raphael Schumacher
This paper presents a family of rapidly convergent summation formulas for various finite sums of the form , where is a positive real number.
Rapidly Convergent Summation Formulas involving Stirling Series
Raphael Schumacher
This paper presents a family of rapidly convergent summation formulas for various finite sums of analytic functions. These summation formulas are obtained by applying a series acce…