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Martin Sleziak
Martin Sleziak
1:08 PM
Borwein integral
In mathematics, a Borwein integral is an integral whose unusual properties were first presented by mathematicians David Borwein and Jonathan Borwein in 2001. Borwein integrals involve products of s i n c ( a x ) {\displaystyle \mathrm {sinc} (ax)} , where the sinc function is given by s i n c ( x ) = sin ⁡ ( x )...
I think I saw som post about this on one of these two sites.
9
Q: Calculating $\int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x / 3)}{x / 3} \frac{\sin(x / 5)}{x / 5} \cdots \frac{\sin(x / 15)}{x / 15} \ dx$

ManyamaI found the following result on this webpage. However, I can't prove if it's true or not. Please tell me how prove it. $$\int_0^{\infty } \left(\prod _{k=0}^7 \frac{\sin \left(\frac{x}{2 k+1}\right)}{\frac{x}{2 k+1}}\right) \, \mathbb{d}x= \frac{\pi}{2} - \frac{6879714958723010531}{935615849440...

integration improper-integrals
198
A: Computer Algebra Errors

Dan PiponiI don't know any interesting bugs in symbolic algebra packages but I know a true, enlightening and entertaining story about something that looked like a bug but wasn't.$\def\sinc{\operatorname{sinc}}$ Define $\sinc x = (\sin x)/x$. Someone found the following result in an algebra package: $\int...

 

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