Given ...

(1)

... and the Euler's constant...

(2)

... demonstrate from definition (2) that is...

(3)

Kind regards

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- Nov 6th 2009, 02:35 AMchisigmaAbout Euler's constant (2)...
Given ...

(1)

... and the Euler's constant...

(2)

... demonstrate from definition (2) that is...

(3)

Kind regards

- Nov 6th 2009, 09:05 AMDrexel28
Prove that if then find__Problem:__

**Proof:**

**Lemma:**Let then

**Proof:**It can be readily seen that . So that . Furthermore . Thus the functional equation and the boundary condition are satisfied

Now using this we can get somehwere. If we look closely at we can see that . Now using the common fact that yields . Now using a litle snake-oil we can see that where . So then or equivalently . So that - Nov 9th 2009, 01:01 AMchisigma
The 'lemma' ...

(1)

... where...

(2)

... must be demonstrated and that can be done with the 'little nice formula' discussed in a previous thread...

(3)

If we compute the integral (3) with applying systematically the integration by parts we obtain...

(4)

Now if we take into account the identity...

(5)

... from (4) we derive the 'infinite product'...

(6)

Kind regards

- Nov 9th 2009, 04:30 AMDrexel28