Carlson Symmetric Form
In mathematics, the Carlson symmetric forms of elliptic integrals are a small canonical set of elliptic integrals to which all others may be reduced. They are a modern alternative to the Legendre forms. The Legendre forms may be expressed in terms of the Carlson forms and vice versa.
The Carlson elliptic integrals are:
Since and are special cases of and, all elliptic integrals can ultimately be evaluated in terms of just and .
The term symmetric refers to the fact that in contrast to the Legendre forms, these functions are unchanged by the exchange of certain of their arguments. The value of is the same for any permutation of its arguments, and the value of is the same for any permutation of its first three arguments.
Read more about Carlson Symmetric Form: Special Cases, Series Expansion, Negative Arguments, Numerical Evaluation, References and External Links
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