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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

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