The error function erf(x) = (2)/(√(π)) ∫^x0 e^-t^2 dt is used in probability, statistics, and engineering. (a) Show that ∫^ba e^-t^2 dt = (1)/(2) √(π) [ erf(b) - erf(a) ] . (b) Show that the function y = e^x^2 erf(x) satisfies the differential equation y' = 2xy 2/√(π) . | Numerade
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The error function erf(x) = (2)/(√(π)) ∫^x0 e^-t^2 dt is used in probability, statistics, and engineering. (a) Show that ∫^ba e^-t^2 dt = (1)/(2) √(π) [ erf(b) - erf(a) ] . (b) Show that the
The error function erf(x) = (2)/(√(π)) ∫^x0 e^-t^2 dt is used in probability, statistics, and engineering. (a) Show that ∫^ba e^-t^2 dt = (1)/(2) √(π) [ erf(b) - erf(a) ] . (b) Show that the function y = e^x^2 erf(x) satisfies the differential equation y' = 2xy 2/√(π) .
Feb 2, 2019
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