DEtools
Gosper
perform indefinite hyperexponential integration
Calling Sequence
Parameters
Description
Examples
References
Gosper(T, x)
T
-
hyperexponential function of x
x
variable
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''.
withDEtools:
T≔−21x2+116x−94−73−35x4−14x3−9x2−51xexp−91−86+5x−−68−7x3+58x2−94x−73−35x4−14x3−9x2−51x2exp−91−86+5x−140x3−42x2−18x−51+455−68−7x3+58x2−94x−73−35x4−14x3−9x2−51x−86+5x2exp−91−86+5x
T≔−21x2+116x−94ⅇ−91−86+5x−35x4−14x3−9x2−51x−73−−7x3+58x2−94x−68ⅇ−91−86+5x−140x3−42x2−18x−51−35x4−14x3−9x2−51x−732+455−7x3+58x2−94x−68ⅇ−91−86+5x−35x4−14x3−9x2−51x−73−86+5x2
IntT,x=GosperT,x
∫−21x2+116x−94ⅇ−91−86+5x−35x4−14x3−9x2−51x−73−−7x3+58x2−94x−68ⅇ−91−86+5x−140x3−42x2−18x−51−35x4−14x3−9x2−51x−732+455−7x3+58x2−94x−68ⅇ−91−86+5x−35x4−14x3−9x2−51x−73−86+5x2ⅆx=7x3−58x2+94x+68ⅇ−91−86+5x35x4+14x3+9x2+51x+73
Almkvist, G, and Zeilberger, D. "The method of differentiating under the integral sign." Journal of Symbolic Computation. Vol. 10 (1990): 571-591.
See Also
DEtools[PolynomialNormalForm]
DEtools[ReduceHyperexp]
DEtools[Zeilberger]
SumTools[Hypergeometric][Gosper]
Download Help Document