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FactorialPower

FactorialPower
gives the factorial power .
FactorialPower
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 .
Find the "factorial square" of 10:
FactorialPower does not automatically expand out:
Use FunctionExpand to do the expansion:
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]=
FactorialPower works with any numbers, not just integers:
Evaluate to arbitrary precision:
The precision of the output tracks the precision of the input:
FactorialPower threads element-wise over lists:
FactorialPower can be expressed in terms of gamma functions:
TraditionalForm formatting:
With step , FactorialPower gives the rising factorial:
FactorialPower can be applied to a power series:
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 :
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