面白い数学の問題おしえて～な 43問目

∫_-∞^∞ exp(-n^2/2) = √(2π)
∫_-∞^∞ exp(-n^2) = √(π)
sum_(n=-∞)^∞ exp(-n^2/2) = ϑ_3(0, 1/sqrt(e))≈2.50663
sum_(n=-∞)^∞ exp(-n^2) = ϑ_3(0, 1/e)≈1.77264
a √(2π) + b √(π) = a ϑ_3(0, 1/sqrt(e)) + b ϑ_3(0, 1/e)
has non trivial roots