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# Getting Pi/2 watch

1. Yesterday someone asked a question about everyone's favorite function, and I posed the challenge to get the result from the Gamma function. I thought this would be a good way to improve my frankly horrible LaTeX skills, I hope I can present Euler's brilliance.

,

we now sub , to get, ,

removing constants we obtain,

we now consider the case that s is complex, which therefore gives us an equation for its conjugate, , that being, ,

we then add/sub the two equations together, ,

then ,

we then define in polar and Cartesian form, so, ,

applying these we get, ,

these reduce to, and , only the second of these we shall use.

That being the second one.

we now set thus meaning ,

we must also use the Euler reflection formula, ,

using what we know, now we get a much more simple formula, ,

now we take the limit as ,

so we have , the right hand side having had some added, but all mathematically consistent.

Evaluating the RHS we get

as we know ,
from this we have,

(typo inevitable, please point out once seen)
2. Woah.
3. LaTeX tips: you'll want to use \sin, \cos, \trig instead of sin, cos, trig which are concantenations variables instead of functions.

You'll want instead of smaller brackets. You do this by using \left( and \right).

Leave a space between the integrand and dx by using \, dx

Great work and nice LaTex skills! Apologies for typo, typing on my phone is hard.

4. I used to understand all this ....
5. (Original post by TeeEm)

I used to understand all this ....
do you miss that type of maths at all? or do you prefer the alevel/beginner undergrad content
6. (Original post by DylanJ42)
do you miss that type of maths at all? or do you prefer the alevel/beginner undergrad content
ask me in the morning ... my head is too fuzzy now!!
7. (Original post by TeeEm)
ask me in the morning ... my head is too fuzzy now!!
sure thing, get some sleep sir, it is getting late
8. (Original post by DylanJ42)
sure thing, get some sleep sir, it is getting late
goodnight !!

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