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10A. Sums & 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 |