Tschirnhausen Transformation
A transformation of a Polynomial equation 
which is of the form 
where 
and 
arePolynomials and 
does not vanish at a root of . The Cubic Equation is a specialcase of such a transformation. Tschirnhaus (1683) showed that a Polynomial of degree 
can be reduced to a formin which the 
and 
terms have 0 Coefficients. In 1786, E. S. Bring showed thata general Quintic Equation can be reduced to the form
In 1834, G. B. Jerrard showed that a Tschirnhaus transformation can be used to eliminate the
, , and 
terms for a general Polynomial equation of degree 
.See also Bring Quintic Form, Cubic Equation
References
Boyer, C. B. A History of Mathematics. New York: Wiley, pp. 472-473, 1968. Tschirnhaus. Acta Eruditorum. 1683.
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- Elliptic Integral
- Elliptic Integral of the First Kind
- Elliptic Integral of the Second Kind
- Elliptic Integral of the Third Kind
- Elliptic Integral Singular Value
- Elliptic Integral Singular Value k1
- Elliptic Integral Singular Value k2
- Elliptic Integral Singular Value k3
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- Elliptic Logarithm
- Elliptic Modular Function
- Elliptic Paraboloid
- Elliptic Partial Differential Equation
- Elliptic Plane
- Elliptic Point
- Elliptic Pseudoprime
- Elliptic Rotation
- Elliptic Theta Function
- Elliptic Torus
- Elliptic Umbilic Catastrophe
- Ellison-Mendès-France Constant
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- Elongated Dipyramid