Sympy's List of Known Infinite Sums

[Damon Turney]

Hi,

MUCH gratitude and appreciation for Sympy here!  One improvement could be a fuller list of infinite sums. For example:

summation(1/((i+b)**2+(a)**2) , (i,-oo, oo))

should evaluate to:

pi/a sinh(2 pi a))/ (-cos(2 pi b) + cosh(2 pi a) )

Is there a master list of infinite sums somewhere?  Ma--m---ica seems to have a big ass list.

Anyway, much thanks for all your work on Sympy.

Damon

[Aaron Meurer]

There isn't really. SymPy's summation code uses a suite of algorithms
that match a wide array of expressions. It would be difficult to make
a list because it is more than just matching against a list of known
sums.

Pattern matching against known summations is something that could be
added (a la manualintegrate), but for this summation, it's likely
there is a more general algorithm dealing with double summations that
could be implemented, for instance, making use of the Poisson
summation formula.

Aaron Meurer

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