cernlife Posted June 14, 2011 Share Posted June 14, 2011 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 Link to comment Share on other sites More sharing options...
Fuzzwood Posted June 14, 2011 Share Posted June 14, 2011 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 Link to comment Share on other sites More sharing options...
khaled Posted July 24, 2011 Share Posted July 24, 2011 (edited) 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, 2011 by khaled Link to comment Share on other sites More sharing options...
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