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I am trying to compute the following integral

Integrate[Exp[Sum[-((cw λ - b[i])^2/(2 σ^2)), {i, 1, n}]], {cw, 0, 1}]

And currently Mathematica outputs

(Sqrt[π/2] σ (Erf[(Sqrt[n] (λ - b[i]))/(Sqrt[2] σ)] + Erf[(Sqrt[n] b[i])/(Sqrt[2] σ)]))/(Sqrt[n] λ)

Which not only is blatantly incorrect (there can be no dependence on i, for one), but also has little connection with my input. If I replace n with an integer in the first expression, the output is the correct result for the integration, but I want the general result with n summands. What am I doing wrong?

Edit: I am willing to make assumptions, such as that λ, σ and all b[i]'s are real. Nonetheless, that does not seem to matter here.

I am trying to compute the following integral:

Integrate[Exp[Sum[-((cw λ - b[i])^2/(2 σ^2)), {i, 1, n}]], {cw, 0, 1}]

And currently Mathematica outputs

(Sqrt[π/2] σ (Erf[(Sqrt[n] (λ - b[i]))/(Sqrt[2] σ)] + 

     Erf[(Sqrt[n] b[i])/(Sqrt[2] σ)]))/(Sqrt[n] λ)

Which is not only blatantly incorrect (there can be no dependence on i for example), but also has little connection with my input. If I replace n with an integer in the first expression, the output is the correct result for the integration, but I want the general result with n summands. What am I doing wrong?

Edit: I am willing to make assumptions, such as that λ, σ and all b[i]'s are real. Nonetheless, that does not seem to matter here.

I am trying to compute the following integral

Integrate[Exp[Sum[-((cw λ - b[i])^2/(2 σ^2)), {i, 1, n}]], {cw, 0, 1}]

And currently Mathematica outputs

(Sqrt[π/2] σ (Erf[(Sqrt[n] (λ - b[i]))/(Sqrt[2] σ)] + Erf[(Sqrt[n] b[i])/(Sqrt[2] σ)]))/(Sqrt[n] λ)

Which not only is blatantly incorrect (there can be no dependence on i, for one), but also has little connection with my input. If I replace n with an integer in the first expression, the output is the correct result for the integration, but I want the general result with n summands. What am I doing wrong?

I am trying to compute the following integral

Integrate[Exp[Sum[-((cw λ - b[i])^2/(2 σ^2)), {i, 1, n}]], {cw, 0, 1}]

And currently Mathematica outputs

(Sqrt[π/2] σ (Erf[(Sqrt[n] (λ - b[i]))/(Sqrt[2] σ)] + Erf[(Sqrt[n] b[i])/(Sqrt[2] σ)]))/(Sqrt[n] λ)

Which not only is blatantly incorrect (there can be no dependence on i, for one), but also has little connection with my input. If I replace n with an integer in the first expression, the output is the correct result for the integration, but I want the general result with n summands. What am I doing wrong?

Edit: I am willing to make assumptions, such as that λ, σ and all b[i]'s are real. Nonetheless, that does not seem to matter here.