08/22/2013, 10:46 PM
(08/22/2013, 05:54 PM)JmsNxn Wrote:
Integrate by parts, and forwe get the spectacular identity that:
I do not even need to use integrate by parts to see a problem.
Its funny you say
because its more like an equality when we differentiate a given amount of times with respect to t.
You see : s is considered a constant with respect to t since s is not a function OF t NOR f.
There is big difference between a function , an operator , a variable and a constant.
ALthough that may sound belittling or trivial , your example shows this is an important concept !!
If you consider
By the chain rule you then get the " wrong " / " correct "
This is similar to
Hence by the very definition of the gamma function you also get
This might not answer all your questions yet but I assume it helps.
It not completely formal either sorry.
It might affect your other posts about integral representations for fractional calculus , tetration and continuum sum.
Im still optimistic though and hope I did not discourage you to much.
regards
tommy1729