DocumentCode
2536341
Title
Automatic Improvements of Wallis´ Inequality
Author
Paule, Peter ; Pillwein, Veronika
Author_Institution
Res. Inst. for Symbolic Comput., Johannes Kepler Univ., Linz, Austria
fYear
2010
fDate
23-26 Sept. 2010
Firstpage
12
Lastpage
16
Abstract
The mathematical backbone of this article is formed by three classical formulas of Wallis: his product formula for π, 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.
Keywords
integral equations; Collins cylindrical algebraic decomposition; Wallis inequality; definite integral; mathematical backbone; product formula; sine function; Algebra; Computers; Design automation; Polynomials; Presses; System-on-a-chip; Upper bound; Wallis integral; Wallis product formula; cylindrical algebraic decomposition; inequalities; symbolic integration; symbolic summation;
fLanguage
English
Publisher
ieee
Conference_Titel
Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2010 12th International Symposium on
Conference_Location
Timisoara
Print_ISBN
978-1-4244-9816-1
Type
conf
DOI
10.1109/SYNASC.2010.89
Filename
5715263
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