In the theory of special functions, a class of functions is said to be "of the third kind" if it is similar to but distinct from previously defined functions
already defined to be of the first and second
kinds. The only common functions of the third kind are the elliptic
integral of the third kind 
and the Bessel function of the third kind (more
commonly called the Hankel function).
Third Kind
See also
Elliptic Integral of the Third Kind, First Kind, Hankel Function, Second Kind, Special FunctionExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Third Kind." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThirdKind.html