Fifth, the probability integral (error function)

[Probability integral definition and series expression]

  Probability Integral (or error function)

  I probability integral (or error function)

  Normal probability integral

 

Called Kummer function)

[Probability integral asymptotic expression]

If the series before and term it as an approximation, the error

When time is a real number, the error does not exceed the absolute value of the first item in the series omitted.

When when .