gives the discrete ratio .
gives the multiple discrete ratio.
gives the multiple discrete ratio with step h.
computes the partial difference ratio with respect to i, j, ….
Details and Options
- DiscreteRatio[f,i] can be input as if. The character is entered dratio or as \[DiscreteRatio]. The variable i is entered as a subscript.
- All quantities that do not explicitly depend on the variables given are taken to have discrete ratio equal to one.
- A multiple discrete ratio is defined recursively in terms of lower discrete ratios.
- Discrete ratio is the inverse operator to indefinite product. »
- DiscreteRatio[f,…,Assumptions->assum] uses the assumptions assum in the course of computing discrete ratios.
Examplesopen allclose all
Basic Examples (4)
Discrete ratio is the inverse operator to Product:
Basic Use (4)
Special Sequences (14)
Factorial functions have rational ratios including FactorialPower:
The ratio of an exponential sequence corresponds to the DifferenceDelta of the exponent:
Hypergeometric terms have rational ratios, so CatalanNumber is a hypergeometric term:
Q-factorial functions have q-rational ratios including QPochhammer:
Products of factorial functions have factorial ratios, including BarnesG:
Hyperfactorial is a product of ii:
The difference of GammaRegularized with respect to is a hypergeometric term:
Similarly for BetaRegularized:
The defining property for a geometric sequence is that its DiscreteRatio is constant:
DiscreteRatio gives the interest rate the compounding sequence:
Compute the DiscreteRatio for this series:
Verify the result using SumConvergence:
The DiscreteRatio of a product is equivalent to the factor:
Verify the solution from RSolve using a higher-step shift ratio:
Properties & Relations (6)
DiscreteRatio distributes over products and integer powers:
Use Ratios to compute ratios of adjacent terms:
Use PowerRange to generate a list with constant ratio:
Wolfram Research (2008), DiscreteRatio, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteRatio.html.
Wolfram Language. 2008. "DiscreteRatio." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteRatio.html.
Wolfram Language. (2008). DiscreteRatio. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteRatio.html