The series are also studied for non-integer values of " n "; these make up the Dirichlet eta function.
12.
It is intimately connected with the polylogarithm, inverse tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function.
13.
Functions such as the Dedekind eta function, a modular form of weight 1 / 2, may be encompassed by the theory by allowing automorphic factors.
14.
An equivalent relationship had been conjectured by Euler over a hundred years earlier, in 1749, for the Dirichlet eta function ( alternating zeta function ):
15.
Our Dirichlet eta function article gives that formula as one definition, which allows for a quick proof :-) Algebraist 16 : 15, 23 April 2007 ( UTC)
16.
The function ? is the Dedekind eta function, and " h " is the class number, and " w " is the number of roots of unity.
17.
Just to be sure, I understand the relation is just the functional equation for the eta function and I have already gone through the proof of that.
18.
When integrating over surfaces such as the torus, we end up with equations in terms of theta functions and elliptic functions such as the Dedekind eta function.
19.
Part of Euler's motivation for studying series related to was the functional equation of the eta function, which leads directly to the functional equation of the Riemann zeta function.
20.
An elementary direct and \ zeta \,-independent proof of the vanishing of the eta function at s _ n \ ne1 was published by J . Sondow in 2003.
