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The co-efficients are given by the following rule:

a0=1

a1=z

a2=z(z-1)

a3=z(z-1)(z-2)

.

.

.

an=z(z-1)(z-2)...(z-(n-1))

where a = any real number

I was thinking of using the following definition, an = z!/(z-n)! which seems to give me the correct results but I am worried about whether or not the ! can be defined on real numbers. Like is there a problem with this definition?