perform indefinite hyperexponential integration - Maple Help

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DEtools[Gosper] - perform indefinite hyperexponential integration

Calling Sequence

Gosper(T, x)

Parameters

T

-

hyperexponential function of x

x

-

variable

Description

• 

The Gosper(T,x) command solves the problem of indefinite hyperexponential integration, that is, for the input hyperexponential function T of x, it constructs another hyperexponential function G of x such that Tx=ⅆⅆxGx, provided that such a G exists. Otherwise, the function returns the error message ``no polynomial solution found''.

Examples

withDEtools:

T:=21x2+116x94ⅇ9186+5x7335x414x39x251x687x3+58x294xⅇ9186+5x140x342x218x517335x414x39x251x2+455687x3+58x294xⅇ9186+5x7335x414x39x251x86+5x2

T:=21x2+116x94ⅇ9186+5x35x414x39x251x737x3+58x294x68ⅇ9186+5x140x342x218x5135x414x39x251x732+4557x3+58x294x68ⅇ9186+5x35x414x39x251x7386+5x2

(1)

∫Tⅆx=GosperT,x

∫21x2+116x94ⅇ9186+5x35x414x39x251x737x3+58x294x68ⅇ9186+5x140x342x218x5135x414x39x251x732+4557x3+58x294x68ⅇ9186+5x35x414x39x251x7386+5x2ⅆx=7x358x2+94x+68ⅇ9186+5x35x4+14x3+9x2+51x+73

(2)

See Also

DEtools, DEtools[PolynomialNormalForm], DEtools[ReduceHyperexp], DEtools[Zeilberger], SumTools[Hypergeometric][Gosper]

References

  

Almkvist, G, and Zeilberger, D. "The method of differentiating under the integral sign." Journal of Symbolic Computation. Vol. 10 (1990): 571-591.


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