Numbers, functions of the first kind, second kind...

[EmptySetBlues]

What is the general scheme by which some related numbers or functions are known as 'of the first kind', 'of the second kind', etc.? I can't seem to find anything about it.

 

[MathLover1]

numbers 'of the first kind'
https://www.whitman.edu/mathematics/cgt_online/book/section01.08.html

Stirling numbers of the first kind
https://www.whitman.edu/mathematics/cgt_online/book/section01.08.html

functions 'of the first kind'
https://www.math.usm.edu/lambers/mat415/lecture12.pdf

functions 'of the second kind'
http://www.math.usm.edu/lambers/mat415/lecture16.pdf

 

[EmptySetBlues]

Thank you. So it appears, then, that functions of the second kind do not have any universal type of relationship to their corresponding functions of the first kind, they are simply related by whatever relationship is of specific interest in each instance. I thought that, as often as I see these phrases, there might be some more general reason why number sets and functions so often occur in such pairings.