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Question: a question on integration of error function function

Question:a question on integration of error function function

mehdi jafari 754 Maple
integration assumptions error-function
August 07 2019
0

how this integral can be calculated in the simplest form ? the second question is what exactly is done when using assuming? for example when using assuming real, all the functions or parameteres are affected? thanks in advanced

 

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restart:with(IntegrationTools):
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(int(int(exp(-(y-beta[0]-beta[1]*x-b0-b1*x)^2/(2*sigma^2))*exp(-b0)*exp(-b1),b0=0..infinity),b1=0..infinity,continuous=true) assuming real)

signum(limit(-(1/2)*Pi^(1/2)*exp((1/2)*(2*b1+2*beta[1])*x+(1/2)*sigma^2-y-b1+beta[0])*2^(1/2)*sigma*(erf((1/2)*(sigma^2+(b1+beta[1])*x-y+beta[0])*2^(1/2)/sigma)-signum(sigma)), b1 = infinity))*infinity

 (1)
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