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Zeitschrift für Analysis und ihre Anwendungen

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Volume 6, Issue 5, 1987, pp. 421–438
DOI: 10.4171/ZAA/261

Published online: 1987-10-31

Über das asymptotische Verhalten des Fermi–Dirac-Integrals

Hans-Joachim Schell

New asymptotic expansions of the Fermi-Dirac integral $F_{p^–1}(x)$ are derived in the case that both $x$ and $p$ tend to infinity: a) for $p \sim x$, b) for $p = ax, 0 < a < 2$. A new asymptotic approximation is given for $p \to \infty, \sqrt p = o(p - 2x)$. The values calculated with these formulas are for several pairs $(x, p)$ compared with the exact values.

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Schell Hans-Joachim: Über das asymptotische Verhalten des Fermi–Dirac-Integrals. Z. Anal. Anwend. 6 (1987), 421-438. doi: 10.4171/ZAA/261