Monday, 17 September 2018

real analysis - Evaluate f(x)=sumi0nftyfracxnn!!.

A question from Introduction to Analysis by Arthur Mattuck:




Let n!!=n(n2)(n4)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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