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    • https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Essential_Graduate_Physics_-_Statistical_Mechanics_(Likharev)/03%3A_Ideal_and_Not-So-Ideal_Gases/3.03%3A_Degenerate_Fermi_gas
      \[\begin{align} I(T) \approx & \int_{0}^{\infty}\left[f(\mu)+\left.\frac{d f}{d \varepsilon}\right|_{\varepsilon=\mu}(\varepsilon-\mu)+\left.\frac{1}{2} \frac{d^{2} f}{d \varepsilon^{2}}\right|_{\vare...\[\begin{align} I(T) \approx & \int_{0}^{\infty}\left[f(\mu)+\left.\frac{d f}{d \varepsilon}\right|_{\varepsilon=\mu}(\varepsilon-\mu)+\left.\frac{1}{2} \frac{d^{2} f}{d \varepsilon^{2}}\right|_{\varepsilon=\mu}(\varepsilon-\mu)^{2}\right]\left[-\frac{\partial\langle N(\varepsilon)\rangle}{\partial \varepsilon}\right] d \varepsilon \nonumber\\ =& \int_{0}^{\mu} \varphi\left(\varepsilon^{\prime}\right) d \varepsilon^{\prime} \int_{0}^{\infty}\left(-\frac{\partial\langle N(\varepsilon)\rangle}{\p…

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