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function_integral_on_ℝⁿ [2016/03/28 20:29]
nikolaj
function_integral_on_ℝⁿ [2017/01/05 00:00] (current)
nikolaj
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 Special case Special case
  
-$$\int_{-a}^a E(x) \left( 1 + \sum_{k=0}^\infty c_k U_k(x)^{2k+1} \right) = \int_0^a E(x) \,{\mathrm d}x$$+$$\int_{-a}^a E(x) \left( ​\dfrac{1}{2} + \sum_{k=0}^\infty c_k U_k(x)^{2k+1} \right) ​\,{\mathrm d}x = \int_0^a E(x) \,{\mathrm d}x$$
  
 e.g. all $U_k$ the same and $c_k$ so that you get $\frac{1}{1\pm e^{y}}$: e.g. all $U_k$ the same and $c_k$ so that you get $\frac{1}{1\pm e^{y}}$:
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