Veronika Elisabeth Pillwein, Peter Paule,
"Automatic Improvements of Wallis' Inequality"
, Serie RISC Report Series, University of Linz, Austria, Nummer 08-18, RISC, JKU-Linz, Schloss Hagenberg, 4232 Hagenberg, 2008
Automatic Improvements of Wallis' Inequality
Sprache des Titels:
The mathematical backbone of this article is formed by three classical formulas of Wallis: his product formula for $\pi$, an inequality implying the product formula in the limit, and a related definite integral involving powers of the sine function. For the latter we present various evaluations to illustrate recent algorithmic developments. In the main part of the article we automatically refine the bounds in Wallis' inequality by using methods based on Collins' cylindrical algebraic decomposition.