The Weierstrass substitution is the trigonometric substitution
into one of the form
According to Spivak (2006, pp. 382-383), this is undoubtably the world's sneakiest substitution.
The Weierstrass substitution can also be useful in computing a Gröbner basis to eliminate trigonometric functions from a system of equations (Trott
2006, p. 39).
See also Gröbner Basis ,
Half-Angle Formulas ,
Hyperbolic Substitution ,
Trigonometric Substitution
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References Anton, H. Calculus: A New Horizon, 6th ed. Spivak,
M. Calculus,
3rd ed. Stewart,
J. Calculus:
Early Transcendentals, 2d ed. Trott,
M. The
Mathematica GuideBook for Symbolics. http://www.mathematicaguidebooks.org/ . Referenced
on Wolfram|Alpha Weierstrass Substitution
Cite this as:
Weisstein, Eric W. "Weierstrass Substitution."
From MathWorld https://mathworld.wolfram.com/WeierstrassSubstitution.html
Subject classifications
which transforms an integral of the form
