Automatic Improvements of Wallis' Inequality

Veronika Pillwein; Peter Paule

Automatic Improvements of Wallis' Inequality

Research Institute for Symbolic Computation

Research output: Working paper and reports › Preprint

Abstract

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.

Original language	English
Place of Publication	Schloss Hagenberg, 4232 Hagenberg
Publisher	RISC, JKU-Linz
Number of pages	10
Publication status	Published - 2008

Publication series

Name	RISC Report Series
No.	08-18

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

@techreport{1069f0807f36437396b44f5a0e8828f2,

title = "Automatic Improvements of Wallis' Inequality",

abstract = "The mathematical backbone of this article is formed by three classical formulas of Wallis: his product formula for \$\textbackslash{}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.",

author = "Veronika Pillwein and Peter Paule",

year = "2008",

language = "English",

series = "RISC Report Series",

publisher = "RISC, JKU-Linz",

number = "08-18",

type = "WorkingPaper",

institution = "RISC, JKU-Linz",

}

TY - UNPB

T1 - Automatic Improvements of Wallis' Inequality

AU - Pillwein, Veronika

AU - Paule, Peter

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

M3 - Preprint

T3 - RISC Report Series

BT - Automatic Improvements of Wallis' Inequality

PB - RISC, JKU-Linz

CY - Schloss Hagenberg, 4232 Hagenberg

ER -