I'm struggling to work out how to integrate the following

 

[latex]\int_0^t(\gamma^{1/\kappa}-i\zeta{w}(1-t/s)_+^{H-1/2})^{\kappa}ds[/latex]

 

here (.)_+ denotes the positive part

 

if I did not have the ^(H-1/2) I can do it, alas it does have it! and so it stumps me on how to evaluate this integral.

 

any advice much appreciated

Cant you split it in several parts? ^H-1/2 is nothing more than something to the power of H multiplied by the same something to the power of -1/2

So,

 

[math]

\int_0^t (\gamma^{1/\kappa}-i\zeta{w}(1-t/s)_+^{H-1/2})^{\kappa}ds = \int_0^t (\gamma^{1/\kappa}-(i\zeta{w}(1-t/s)_+^{H} \times i\zeta{w}(1-t/s)_+^{-1/2}))^{\kappa}ds

[/math]

 

[math]

= \int_0^t (\frac{\sqrt[\kappa]{\gamma} - (i\zeta{w}(1-t/s)_+^{H}}{\sqrt{i\zeta{w}(1-t/s)_+})})^{\kappa} ds

[/math]

Edited July 24, 201114 yr by khaled