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Let $f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$,
defined inside the unit square.
Then we have $f(\alpha, \beta)=f(\beta, \alpha)$

  But why? A mystery so deep it will never be uncovered. Its not provable. We are looking into the symmetric eyes of God.

Reference  : https://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral

Let $$f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$$
defined inside the unit square. Then we have $f(\alpha, \beta)=f(\beta, \alpha)$. But why?

Reference: https://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral

Let $f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$,
defined inside the unit square.
Then we have $f(\alpha, \beta)=f(\beta, \alpha)$

But why? A mystery so deep it will never be uncovered. Its not provable. We are looking into the symmetric eyes of God.

Reference : http://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral

Let $f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$,
defined inside the unit square.
Then we have $f(\alpha, \beta)=f(\beta, \alpha)$

But why? A mystery so deep it will never be uncovered. Its not provable. We are looking into the symmetric eyes of God.

Reference : https://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral

Let $f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$,
defined inside the unit square.
Then we have $f(\alpha, \beta)=f(\beta, \alpha)$

But why? A mystery so deep it will never be uncovered. Its not provable. We are looking into the symmetric eyes of God.

Let $f(\alpha, \beta) = \int_0^{\infty} dx \: \frac{x^{\alpha}}{1+2 x \cos{(\pi \beta)} + x^2}$,
defined inside the unit square.
Then we have $f(\alpha, \beta)=f(\beta, \alpha)$

But why? A mystery so deep it will never be uncovered. Its not provable. We are looking into the symmetric eyes of God.

Reference : http://math.stackexchange.com/questions/268789/symmetry-of-function-defined-by-integral