The integral of the first kind he wrote on the symmetric form
2.
Abel wrote an integral of the first kind as
3.
An elliptic integral of the first kind can be used to solve for " w ".
4.
The integral may also be recognized as a multiple of Legendre's complete elliptic integral of the first kind.
5.
Euler integral of the second kind "'( the Euler integral of the first kind defines the beta function ).
6.
Where is the maximum angle of oscillation ( with respect to the vertical ) and is the complete elliptic integral of the first kind.
7.
There is a simpler, but completely equivalent definition, giving the elliptic functions as inverses of the incomplete elliptic integral of the first kind.
8.
Borwein and Zucker have found that ) } } can be expressed algebraically in terms of,,,, and where is a complete elliptic integral of the first kind.
9.
In 1917 he published his dissertation in mathematics " Ensimm�isen lajin elliptisen integralin k��nteisfunktion yksik�sitteisyys " ( The single-valuedness of the inverse function of the elliptic integral of the first kind ).
10.
For example, the first example s integral is expressible using incomplete elliptic integrals of the first kind, the second and third use the logarithmic integral, the fourth the exponential integral, and the sixth the error function.
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