FactorialPower

FactorialPower[x,n]

gives the factorial power .

FactorialPower[x,n,h]

gives the step-h factorial power .

Details

  • 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 .
  • TemplateBox[{TemplateBox[{x, k}, FactorialPower], x}, DifferenceDelta2] is given by k TemplateBox[{x, {k, -, 1}}, FactorialPower] and sum_xTemplateBox[{x, k}, FactorialPower] is given by TemplateBox[{x, {k, +, 1}}, FactorialPower]/(k+1).
  • FactorialPower[x,n] evaluates automatically only when x and n are numbers.
  • FunctionExpand always converts FactorialPower to a polynomial or combination of gamma functions.

Examples

open allclose all

Basic Examples  (2)

Find the "factorial square" of 10:

In[1]:=
Click for copyable input
Out[1]=

FactorialPower does not automatically expand out:

In[1]:=
Click for copyable input
Out[1]=

Use FunctionExpand to do the expansion:

In[2]:=
Click for copyable input
Out[2]=

Scope  (5)

Generalizations & Extensions  (2)

Applications  (2)

Properties & Relations  (7)

Possible Issues  (2)

See Also

Factorial  Gamma  Pochhammer  Binomial  Power  Sum  DifferenceDelta  DiscreteRatio  InterpolatingPolynomial

Introduced in 2008
(7.0)