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6

The expression in question is (we have replaced sigma by s) g = Integrate[ Exp[-(x - y)^2/(2 y s^2)] f[y] 1/Sqrt[2 \[Pi] y s^2], {y, 0, \[Infinity]}] $\int_0^{\infty } \frac{e^{-\frac{(x-y)^2}{2 s^2 y}} f[y]}{\sqrt{2 \pi } \sqrt{s^2 y}} \, dy$ First of all we notice that for y>0 "Limit[Exp[-(x - y)^2/(2 y s^2)] 1/Sqrt[2 \[Pi] y s^2], s -> 0] = ...

3

Perhaps better: NMinimize[{m/(m (1 - c) + 1), 2^(m*(1 - c)) - 2.718/((m^.5)*2*3.14*c^(c*m + .5)*(1 - c)^((1 - c)*m + .5)) <= 0 && 0.006 <= c <= 1 && 4 <= m <= 2500}, {m, c}, MaxIterations -> 300] (* {1.11184, {m -> 4., c -> 0.350592}} *)

1

My earlier answer resulting from misreading the question. Taken at face value, you are asking for sum=Sum[3 - 4/(1 - (-3)^(n + 1)), {n, 1436, 2015}] which produces a rationale number with an enormous number of digits. It is, however, almost precisely equal to 3*(2015 - 1436 + 1), or 1740, as one would expect. N[sum,1000] (* ...

1

Did you try using assumptions? Using assumptions with version 10.0.0, I get the same results as with version 10.0.2 \$Version "10.0 for Mac OS X x86 (64-bit) (June 29, 2014)" Clear[f] f[n_Integer] = Integrate[HermiteH[n, x]*Exp[-x^2], {x, 0, Infinity}, Assumptions -> {Element[n, Integers]}] (2^(-1 + n)*Sqrt[Pi])/Gamma[1 - n/2] ...

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