Cancellation of factorials

@article{Zudilin2000CancellationOF,
  title={Cancellation of factorials},
  author={Wadim Zudilin},
  journal={arXiv: Number Theory},
  year={2000}
}
  • W. Zudilin
  • Published 2000
  • Mathematics
  • arXiv: Number Theory
We study the arithmetic property which allows to sharpen number-theoretic estimates. Previous results on this property are, as a rule, quantitive. The application of our general qualitive theorems to generalized hypergeometric functions extends the set of irrational numbers which are the values of these functions. 
4 Citations
Irrationality measure of the number
Using a new integral construction combining the idea of symmetry suggested by Salikhov in 2007 and the integral introduced by Marcovecchio in 2009, we obtain a new bound for the irrationality measureExpand
Arithmetic of linear forms involving odd zeta values
The story exposed in this paper starts in 1978, when R. Apery [Ap] gave a surprising sequence of exercises demonstrating the irrationality of ζ(2) and ζ(3). (For a nice explanation of Apery’sExpand
An Apery-like Difference Equation for Catalan's Constant
  • W. Zudilin
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 2003
TLDR
Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan’s constant with rational coecients, a second-order dierence equation is obtained and a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it is derived. Expand

References

Exponential sums and di?erential equations
This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differentialExpand