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October 30

Gamma function and factorial notation

Squircle#Area has the equation string

\mathrm {Area} =4r^{2}{\frac {\left(\Gamma \left(1+{\tfrac {1}{4}}\right)\right)^{2}}{\Gamma \left(1+{\tfrac {2}{4}}\right)}}={\frac {8r^{2}{\big (}\Gamma {\big (}{\frac {5}{4}}{\big )}{\big )}^{2}}{\sqrt {\pi }}}=4r^{2}{\frac {{\tfrac {1}{4}}!^{2}}{{\tfrac {1}{2}}!}}\approx 3.708r^{2}

Is using the ! sign on a fraction considered acceptable use of the ! notation? Loraof (talk) 01:28, 30 October 2017 (UTC)[reply]

Conventions vary. It's certainly not unheard of to write (1/2)! to mean Γ(3/2), but many authors avoid it. --Trovatore (talk) 01:39, 30 October 2017 (UTC)[reply]

Even if it is acceptable, it seems a little strange to me to switch notation like that in the middle of the equation. If already using the Gamma notation, why not just stick with it till the end? AlfonsoAnonymous (talk) 22:54, 30 October 2017 (UTC)[reply]

You’re right – I’m going to delete it. Loraof (talk) 23:19, 30 October 2017 (UTC)[reply]

Region bounded by ax^2 + by^4 + cz^6 = 1

Does this shape have a name? An example for a=1, b=2, c=3. 68.0.147.114 (talk) 21:49, 30 October 2017 (UTC)[reply]

Superquadric, although our article can’t decide whether that is the surface or the region – I’ll tweak it a little to point out the distinction. Loraof (talk) 23:31, 30 October 2017 (UTC)[reply]

Is there a general expression for the volume? 68.0.147.114 (talk) 00:21, 31 October 2017 (UTC)[reply]

Superellipsoid has a formula for the ~~area~~ volume if all the exponents are identical (the article’s special case of t=r). For different exponents I can’t find anything. Loraof (talk) 01:03, 31 October 2017 (UTC)[reply]