Legendary Chi function
The legendary Chi function (after Adrien-Marie Legendre ) is a special function in mathematics .
definition
The legendary chi function is defined as follows:
It can also be expressed with the polylogarithm :
Special values
with the imaginary unit and the Catalan constant .
Special cases and generalizations
The Dirichlet Lambda function is one of the special cases
and the Dirichlet beta function :
The transcendent Lerchian zeta function generalizes the legendary Chi function:
See also
credentials
- Eric W. Weisstein : Legendre's Chi Function . In: MathWorld (English).
- Djurdje Cvijović and Jacek Klinowski, " Values of the Legendre chi and Hurwitz zeta functions at rational arguments ", Math. Of Comp. 68: 1623-1630 (1999).