Compute the discrete ratio:
The second discrete ratio:
Explicit shift structure in the function will typically be canceled:
Compute the discrete ratio of step h:
The second discrete ratio of step h:
Compute the partial discrete ratio:
Mix any orders:
Or any steps:
Polynomial functions:
An explicit shift structure between roots cancels:
FactorialPower and
Pochhammer have an explicit shift structure:
Rational functions:
Explicit shift ratio cancels:
Exponential functions:
DiscreteRatio of exponentials is closely related to
DifferenceDelta:
Polynomial exponents:
Hypergeometric terms are defined by having a rational discrete ratio:
CatalanNumber is a hypergeometric term:
Q-polynomial functions:
An explicit shift structure in the exponents and roots cancels:
QPochhammer has an explicit shift structure:
Q-rational functions:
An explicit shift structure in exponents and roots cancels:
QBinomial has explicit shift structure:
Q-hypergeometric terms are defined by having a q-rational discrete ratio:
BarnesG is a product of
Gamma functions:
The second discrete will be rational:
Hyperfactorial is a product of
:
A multivariate hypergeometric term is hypergeometric in each variable:
The binomial distribution is a multivariate hypergeometric term:
DiscreteRatio is the inverse operator to
Product:
Definite products:
Other special operators:
In this case the variable x is scoped:
.
can be input as 
. The character 
is entered Esc dratio Esc or as \[DiscreteRatio]. The variable i is entered as a subscript.
using Esc dratio Esc, and subscripts using Ctrl+_:
:
EXAMPLES
Basic Examples 
Scope 