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Weierstrass Form


There are (at least) two mathematical objects known as Weierstrass forms. The first is a general form into which an elliptic curve over any field K can be transformed, given by

 y^2+ay=x^3+bx^2+cxy+dx+e,

where a, b, c, d, and e are elements of K.

The second is the definition of the gamma function as

 Gamma(z)=[ze^(gammaz)product_(r=1)^infty(1+z/r)e^(-z/r)]^(-1),

where gamma is the Euler-Mascheroni constant (Krantz 1999, p. 157).


See also

Elliptic Curve, Gamma Function

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References

Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 57, 2003.Krantz, S. G. "The Gamma and Beta Functions." §13.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 155-158, 1999.

Referenced on Wolfram|Alpha

Weierstrass Form

Cite this as:

Weisstein, Eric W. "Weierstrass Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeierstrassForm.html

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