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RationalNormalForms

  

MinimalRepresentation

  

construct the first and second minimal representations of a hypergeometric term

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

MinimalRepresentation[1](H, n, k)

MinimalRepresentation[2](H, n, k)

Parameters

H

-

hypergeometric term in n

n

-

variable

k

-

name

Description

• 

The MinimalRepresentation[1](H,n,k) and MinimalRepresentation[2](H,n,k) functions construct the first and second minimal representations for H, where H be a hypergeometric term in n. respectively.

• 

If Hn is a hypergeometric term such that Hn+1Hn=Rn, a rational function in n for all n0n, then Hn=Hn0k=n0n1Rk, n0n. If z,r,s,u,v is a rational normal form of Rn, then Hn=Hn0znFnk=n0n1rkskzn0Fn0, where F=uv.

  

Note: rk and sk are of minimal possible degrees.

• 

The first and second minimal representations of Hn are constructed from the first and second canonical forms of Rn, respectively.

• 

This function is part of the RationalNormalForms package, and so it can be used in the form MinimalRepresentation(..) only after executing the command with(RationalNormalForms). However, it can always be accessed through the long form of the command by using RationalNormalForms[MinimalRepresentation](..).

Examples

withRationalNormalForms:

Hn213n+1!n+3!2n+7!

Hn213n+1!n+3!2n+7!

(1)

MinimalRepresentation1H,n,k

274nn1k=2n1k+23k+43k+4k+92721710n+3n+2

(2)

MinimalRepresentation2H,n,k

4274nk=2n1k+23k+43k+92k124057n+32n+22n+1n

(3)

References

  

Abramov, S., and Petkovsek, M. "Canonical Representations of Hypergeometric Terms." In Proceedings of FPSAC '01, 1-10. Edited by H. Barcelo and V. Welker. Tucson: University of Arizona Press, 2001.

See Also

RationalNormalForms[IsHypergeometricTerm]

RationalNormalForms[RationalCanonicalForm]