Question: Is there a way to convert integral of "erf" function into normal cumulative distribution function?

Hi all,

In Maple, I am integrating a function involving the "erfc" function,

the final integral result has no explicit form, but should be able to
representted as a "\Phi(.)" function, where the "\Phi(.)" is the Gaussian
distribution function (cumulative).

Is there a way to force the following integral to output in the form of
"\Phi(.)" in Maple?

Thanks

int(exp(a*m)*(sqrt(T)*sqrt(Pi)*erf((1/2)*sqrt(2)*(m+a*T)/sqrt(T))*exp(a*m)*a-sqrt(T)*sqrt(Pi)*exp(a*m)*a+sqrt(2)*exp(-(1/2)*(m^2+a^2*T^2)/T)),
m = 0 .. K)


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I got some simple result in terms of "\Phi" function by manual calculation. But since there are many more complicated terms, I would like to see what can Maple get and later I can use Maple to check my calculations...

 

 

 

 

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