| . | |$\alpha \leq 2b^2/a^2$| . | 2b2/a2 < α < 2 . | α = 2 . | 2 < α < 3 . |
|---|---|---|---|---|
| . | |$(k_\alpha \geq 1-b^2/a^2)$| . | (0 < kα < 1 − b2/a2) . | (kα = 0) . | (− 1/2 < kα < 0) . |
| fα | 1 | |$\left[\sin (\pi /\alpha)\right]^{\alpha /(\alpha -2)}$| | ||
| Aα | |$\left(2/k_\alpha ^2\right) \sin ^2(k_\alpha \pi /4)$| | |$\pi ^2/8$| | |$\left(1/2k_\alpha ^2\right) \cot ^2(\pi /\alpha)$| | |
| ζ | |$(1/k_\alpha)\left[(z_{\rm c}/a)^{k_\alpha }-1\right]$| | ln (zc/a) | |$(-1/k_\alpha)\left[(z_{\rm c}/a)^{-k_\alpha }-1\right]$| | |
| Bulge forms? | No | Yes | ||
| Asymptotic shape | Sphere | ‘Peanut’ | ||
| . | |$\alpha \leq 2b^2/a^2$| . | 2b2/a2 < α < 2 . | α = 2 . | 2 < α < 3 . |
|---|---|---|---|---|
| . | |$(k_\alpha \geq 1-b^2/a^2)$| . | (0 < kα < 1 − b2/a2) . | (kα = 0) . | (− 1/2 < kα < 0) . |
| fα | 1 | |$\left[\sin (\pi /\alpha)\right]^{\alpha /(\alpha -2)}$| | ||
| Aα | |$\left(2/k_\alpha ^2\right) \sin ^2(k_\alpha \pi /4)$| | |$\pi ^2/8$| | |$\left(1/2k_\alpha ^2\right) \cot ^2(\pi /\alpha)$| | |
| ζ | |$(1/k_\alpha)\left[(z_{\rm c}/a)^{k_\alpha }-1\right]$| | ln (zc/a) | |$(-1/k_\alpha)\left[(z_{\rm c}/a)^{-k_\alpha }-1\right]$| | |
| Bulge forms? | No | Yes | ||
| Asymptotic shape | Sphere | ‘Peanut’ | ||
| . | |$\alpha \leq 2b^2/a^2$| . | 2b2/a2 < α < 2 . | α = 2 . | 2 < α < 3 . |
|---|---|---|---|---|
| . | |$(k_\alpha \geq 1-b^2/a^2)$| . | (0 < kα < 1 − b2/a2) . | (kα = 0) . | (− 1/2 < kα < 0) . |
| fα | 1 | |$\left[\sin (\pi /\alpha)\right]^{\alpha /(\alpha -2)}$| | ||
| Aα | |$\left(2/k_\alpha ^2\right) \sin ^2(k_\alpha \pi /4)$| | |$\pi ^2/8$| | |$\left(1/2k_\alpha ^2\right) \cot ^2(\pi /\alpha)$| | |
| ζ | |$(1/k_\alpha)\left[(z_{\rm c}/a)^{k_\alpha }-1\right]$| | ln (zc/a) | |$(-1/k_\alpha)\left[(z_{\rm c}/a)^{-k_\alpha }-1\right]$| | |
| Bulge forms? | No | Yes | ||
| Asymptotic shape | Sphere | ‘Peanut’ | ||
| . | |$\alpha \leq 2b^2/a^2$| . | 2b2/a2 < α < 2 . | α = 2 . | 2 < α < 3 . |
|---|---|---|---|---|
| . | |$(k_\alpha \geq 1-b^2/a^2)$| . | (0 < kα < 1 − b2/a2) . | (kα = 0) . | (− 1/2 < kα < 0) . |
| fα | 1 | |$\left[\sin (\pi /\alpha)\right]^{\alpha /(\alpha -2)}$| | ||
| Aα | |$\left(2/k_\alpha ^2\right) \sin ^2(k_\alpha \pi /4)$| | |$\pi ^2/8$| | |$\left(1/2k_\alpha ^2\right) \cot ^2(\pi /\alpha)$| | |
| ζ | |$(1/k_\alpha)\left[(z_{\rm c}/a)^{k_\alpha }-1\right]$| | ln (zc/a) | |$(-1/k_\alpha)\left[(z_{\rm c}/a)^{-k_\alpha }-1\right]$| | |
| Bulge forms? | No | Yes | ||
| Asymptotic shape | Sphere | ‘Peanut’ | ||
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