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Going through a world of adventure from Feynman's tricks, infinite series (Dirichlet's beta function) and many more to develop the solution of this fun little integral. Full solution development included..
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Starting with Taylor series of the integral and through use of Legendre Duplication formula and Bessel function series to develop solutions to couple of trig functions integrals. Full solution
included..
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Here's a good approximation for this infinite product. The absolute error approaches zero for larger values of 'a' value. Full solution development included...
