SumTools[Hypergeometric] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Discrete Mathematics : Summation and Difference Equations : SumTools : Hypergeometric Subpackage : SumTools/Hypergeometric/LowerBound

SumTools[Hypergeometric]

  

LowerBound

  

compute a lower bound for the order of the telescopers for a hypergeometric term

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

LowerBound(T, n, k, En, 'Zpair')

Parameters

T

-

hypergeometric term in n and k

n

-

name

k

-

name

En

-

(optional) name denoting the shift operator with respect to n

'Zpair'

-

(optional) name

Description

• 

Let T be a hypergeometric term in n and k. The function LowerBound(T, n, k) computes a lower bound for the order of the telescopers for T if it is guaranteed that Zeilberger's algorithm is applicable to T.

• 

If the fourth and the fifth optional arguments (each of which can be any name), En and 'Zpair' respectively, are specified, the minimal telescoper for T is computed and assigned to the fifth argument 'Zpair' using the computed lower bound  as the starting value of the guessed orders.

Examples

withSumToolsHypergeometric:

T1nk+1+1binomial2n,k+11nk+1binomial2n,k+12k1n3k+1binomial2n,k

T2nk+1nk+1+12nknk+1+2nk2k1n3k+1

(1)

LowerBoundT,n,k

3

(2)

Zeilberger's algorithm is not applicable to the following hypergeometric term so LowerBound returns an error.

T1nk+1binomial2n,2k

T2n2knk+1

(3)

LowerBoundT,n,k

Error, (in SumTools:-Hypergeometric:-LowerBound) Zeilberger's algorithm is not applicable

T1nk+11n3k52n+k+4!1nk1n3k22n+k+3!+1n3k22n+k+3!

T1nk+11n3k52n+k+4!1nk1n3k22n+k+3!+1n3k22n+k+3!

(4)

LowerBoundT,n,k,En,Zpair

3

(5)

LZpair1

L96889010407n134013973288290n1276107306338070n11874305244269093n106788048750132832n937604322096371100n8152885294205849709n7461743890026242439n61035633823402072251n51703061496353656040n41995094474254403011n31575944956962320238n2751943328788699320n163575961093126400En4+96889010407n13+3917084277883n12+72536254240212n11+814487155639857n10+6186007839562887n9+33550538764167390n8+133652029105976437n7+395832377416110838n6+871303942188476181n5+1407347883183343752n4+1620685980982353516n3+1259506839996666240n2+591742636413140800n+126860211237760000En3+257298363n6+3969746172n5+25015702068n4+82342227429n3+149184720027n2+140923968318n+54171659763En257298363n65513536350n548723908373n4227248464681n3589862551887n2807775419969n455865322140

(6)

The computed lower bound is 3, while the order of the minimal telescoper is

degreeL,En

4

(7)

References

  

Abramov, S.A. and Le, H.Q. "A Lower Bound for the Order of Telescopers for a Hypergeometric Term." CD-ROM. Proceedings FPSAC 2002. (2002).

See Also

SumTools[Hypergeometric]

SumTools[Hypergeometric][IsZApplicable]

SumTools[Hypergeometric][MinimalZpair]

SumTools[Hypergeometric][Zeilberger]

SumTools[Hypergeometric][ZpairDirect]