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