chapter 30

60 Pages

## - Special Functions and Their Properties

C0a = 1, C k a =

(a k

) = (−1)k (−a)k

k! =

a(a− 1) . . . (a− k + 1) k!

, where k = 1, 2, . . .

Here a is an arbitrary real number.

◮ Generalization. Some properties.

General case:

Cba = Γ(a+ 1)

Γ(b+ 1)Γ(a− b+ 1) , where Γ(x) is the gamma function.