-The derivative with respect to beta, for the following definite integral is required.
g = $\int_\beta^{\sqrt(\beta^2 +1}$ $erfc(\gamma z)/\sqrt(z^2 - \beta^2)$dz
-I am using the leibniz formula given here: http://mathworld.wolfram.com/LeibnizIntegralRule.html
-To calculate the leibniz integral I need the function value at the lower limit which is beta. The function has a singularity at this value.
-My idea was to use a taylor series expansion for approximating the limiting value of the function at beta. Is that a correct approach?
Question: Is there any other way this could be done and if this approach of calculating the derivative of the integral using the leibniz formula correct at all?
Any suggestions will be appreciated.
Thanks