Weierstrass Substitution

The Weierstrass substitution is the trigonometric substitution t=tan(theta/2) which transforms an integral of the form


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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Anton, H. Calculus: A New Horizon, 6th ed. New York: Wiley, pp. 518-519, 1999.Spivak, M. Calculus, 3rd ed. Cambridge, England: Cambridge University Press, 2006.Stewart, J. Calculus: Early Transcendentals, 2d ed. Brooks/Cole, p. 439, 1991.Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, 2006.

Referenced on Wolfram|Alpha

Weierstrass Substitution

Cite this as:

Weisstein, Eric W. "Weierstrass Substitution." From MathWorld--A Wolfram Web Resource.

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