\(=-\frac{2e^{2\ G\ H}}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\left(1-\frac{\text{G\ H}}{w^{2}}\right)\ e^{\left(G\ H/w\right)^{2}-\left(w+G\ H/w\right)^{2}}\text{\ dw}}\) |
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\(=-\frac{2e^{2\ G\ H}}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\left(1-\frac{\text{G\ H}}{w^{2}}\right)\ e^{\left(G\ H/w\right)^{2}-{w^{2}-2\ G\ H-\left(G\ H/w\right)}^{2}}\text{\ dw}}\) |
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\(=-\frac{2e^{2\ G\ H}}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\left(1-\frac{\text{G\ H}}{w^{2}}\right)\ e^{-w^{2}-2\ G\ H}\text{\ dw}}\) |
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\(=-\frac{2}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\left(1-\frac{\text{G\ H}}{w^{2}}\right)\ e^{-w^{2}}\text{\ dw}}\) |
(33) |