Bring-Jerrard Quintic Form
المؤلف:
Grunert, J. A
المصدر:
"VIII. Miscellen von dem Herausgeber." Archiv der Math. Phys. 41
الجزء والصفحة:
...
17-1-2019
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Bring-Jerrard Quintic Form
A Tschirnhausen transformation can be used to algebraically transform a general quintic equation to the form
 |
(1)
|
In practice, the general quintic is first reduced to the principal quintic form
 |
(2)
|
before the transformation is done. Then, we require that the sum of the third powers of the roots vanishes, so
. We assume that the roots 
of the Bring-Jerrard quintic are related to the roots 
of the principal quintic form by
 |
(3)
|
In a similar manner to the principal quintic form transformation, we can express the coefficients 
in terms of the 
.
REFERENCES:
Grunert, J. A. "VIII. Miscellen von dem Herausgeber." Archiv der Math. Phys. 41, 105-112, 1864.
Klein, F. "Über die Transformation der elliptischen Funktionen und die Auflösung der Gleichungen fünften Grades." Math. Ann.14, 111-172, 1878-79.
Tortolini, B. "Rivista bibliografica sopra a transformazione del Sig. Jerrard per l'equazioni di quinto grado." Annali di Mat. pura appl. 6, 33-42, 1864.
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