This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

FactorialPower

 FactorialPower gives the factorial power . FactorialPowergives the step-h factorial power .
• Mathematical function, suitable for both symbolic and numeric manipulation.
• For integer n, is given by , and is given by .
• is given for any n by .
• is given by and is given by .
Find the "factorial square" of 10:
FactorialPower does not automatically expand out:
Use FunctionExpand to do the expansion:
Find the "factorial square" of 10:
 Out[1]=

FactorialPower does not automatically expand out:
 Out[1]=
Use FunctionExpand to do the expansion:
 Out[2]=
 Scope   (5)
FactorialPower works with any numbers, not just integers:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
FactorialPower can be expressed in terms of gamma functions:
With step , FactorialPower gives the rising factorial:
FactorialPower can be applied to a power series:
 Applications   (2)
The number of triples of distinct digits:
Approximate a function using Newton's forward difference formula []:
Construct an approximation by truncating the series:
FactorialPower satisfies :
FactorialPower can always be expressed as a ratio of gamma functions:
Compare to the expansion of :
FactorialPower is equivalent to x!:
The rising factorial is equivalent to a Pochhammer symbol:
Generically, Power is recovered as a limit of of FactorialPower:
This may not be true, however, if is kept on the negative real axis:
Generic series expansion around the origin may not be defined at integer points:
Use assumptions to refine the result:
Compare to expansion for explicit value of :
New in 7