gives the factorial power .
gives 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 .
- FactorialPower[x,n] evaluates automatically only when x and n are numbers.
- FunctionExpand always converts FactorialPower to a polynomial or combination of gamma functions.
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Basic Examples (7)
Numerical Evaluation (4)
Specific Values (5)
Function Properties (4)
Series Expansions (2)
Find the Taylor expansion using Series:
Generalizations & Extensions (2)
Approximate a function using Newton's forward difference formula [MathWorld]:
Properties & Relations (7)
FactorialPower satisfies :
FactorialPower can always be expressed as a ratio of gamma functions:
FactorialPower[x,x] is equivalent to x!:
The rising factorial is equivalent to a Pochhammer symbol:
The generating function for FactorialPower:
The exponential generating function for FactorialPower: