sum n=0 to inf (-1)^n BesselJ(n,a n) is rational for some values of a rational
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with maybe a /it seems that/, but I don't have a method to prove it.
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I suspect that they can be proved by solving a differetial equation with respect to a/b if convergence is guaranteed. ingredients: http://functions.wolfram.com/Bessel-TypeFunctions/BesselJ/20/ShowAll.html … (w.r.t z)
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