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# 10A. Sums and Means

`m0=: A=: # %~ +/` | Arithmetic mean
`m1=: G=: # %: */` | Geometric mean
`m2=: H=: A&.(%"_)` | Harmonic mean
`m3=: C=: [: {. (A,G)^:_` | Common mean; arithmetic-geometric mean (de Kerf [2])
`m4=: A&(^&3)` | Mean of cubes
`a5=: (^&) (A&)` | Generalized x-mean
`m6=: m4 -: 3 a5` | Tautology
`a7=: (^&) (A&.)` | L-x norm
`m8=: (^&3)@(3 a7) -: (3 a5)` | Tautology
`v9=: MA=: A\` | x-period moving average of `y`
`m10=: +/\ -: +/\.&.|.` | Tautology: invariance under reverse
`m11=: +/\. -: +/\ &.|.` | Tautology: invariance under reverse
`m12=: +/\^:(i.`($&1))` | Figurate numbers
`m13=: 1: #. ]` | Sum; `+/"1`
`m14=: +/&.(*:"_)@:+."0` | Magnitude `|`
`m15=: - |.!.0` | `.+/\^:_1`
`d16=: psum=: ([:+/ [ ^~ i.@])"0` | Sum of powers of integers; 2 sum 7
`m17=: 0&psum -: [` | Tautology: `+/(i.n)^0`
`m18=: 1&psum -: 2&!` | Tautology: `+/(i.n)^1`
`m19=: 2&psum -: 0 1r6 _1r2 1r3&p.` | Tautology: `+/(i.n)^2`
`m20=: [ (psum %. ^/~@]) i.@(2&+)` | Polynomial coeff. of `+/(i.n)^k`

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