A question from Introduction to Analysis by Arthur Mattuck:
Let n!!=n(n−2)(n−4)⋅…⋅k, where k=1 or 2,depending on whether n is odd or even. (define 0!!=1.)
Evaluate the sum f(x)=∑∞0xnn!!, using term-by-term differentiation and integration.
I think what the question asked is to give an explicit form for this sum.
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