66The Riemann Zeta function is
\zeta(s):=\sum_{k=1}^\infty \dfrac{1}{k^s}
For s>1, the following relation holds:
\zeta(s)=\dfrac{1}{\Gamma(s)}\int_0^\infty \dfrac{x^{s-1}}{e^x-1}\ \mathrm dx
relaxing, i came about this term!!
GAMMA FUNCTION!!
can anyone explain its meaning???
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2 Answers
62\Gamma (x)=\int_{0}^{\infty}{t^{x-1}e^{-t}dt}
This is as important a function in statistics as in Mathematics.. probably more imp in statistics...
there can be some good passage type questions that can be made out of them even for IIT JEE inspite of the fact that this topic is not in syllabus directly
You may know the value of this function at integers, \Gamma (n)=\int_{0}^{\infty}{t^{x-1}e^{-t}dt}
and the reccurance relation .... That part is important in terms of IIT JEE
And its value when x=1/2
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