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Student Support Forum: 'Finite Sum' topicStudent Support Forum > General > Archives > "Finite Sum"

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Ratna Bandila
10/14/03 4:32pm

I am unable to fing the closed-form expression for
Sum[1/(m1!*m2!*m3!)^2],where m1+m2+m3=n

Mathematica does gives the result for
Sum[1/(m1!*m2!)^2],where m1+m2=n
as
(4^n*Gamma[n+(1/2)])/(Sqrt[pi]*Gamma[n+1]^3])
It also gives the closed-form formula for
Sum[1/(m1!*m2!*m3!)],where m1+m2+m3=n
Sum[1/(m1!*m2!*m3!*m4!)],where m1+m2+m3+m4=n
Sum[1/(m1!*m2!*m3!*m4!*m5!)],where m1+m2+m3+m4+m5=n
....and so on.

Kindly help if anyone has come across the expression.

Thanks
Ratna




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