Sum (Built-in Mathematica Symbol)

Sum[f, {i, i_max}] evaluates the sum \[Sum]i = 1 i_max f. Sum[f, {i, i_min, i_max}] starts with i = i_min. Sum[f, {i, i_min, i_max, di}] uses steps d i. Sum[f, {i, {i_1, i_2, ...

SolveAlways (Built-in Mathematica Symbol)

SolveAlways[eqns, vars] gives the values of parameters that make the equations eqns valid for all values of the variables vars.

Through (Built-in Mathematica Symbol)

Through[p[f_1, f_2][x]] gives p[f_1[x], f_2[x]]. Through[expr, h] performs the transformation wherever h occurs in the head of expr.

Operators (Mathematica Tutorial)

Some operators used in basic arithmetic and algebra. Note that the  for ∖[Cross] is distinguished by being drawn slightly smaller than the × for ∖[Times]. Interpretation of ...

Variance (Built-in Mathematica Symbol)

Variance[list] gives the sample variance of the elements in list. Variance[dist] gives the variance of the symbolic distribution dist.

DirichletCharacter (Built-in Mathematica Symbol)

DirichletCharacter[k, j, n] gives the Dirichlet character \[Chi] {k, j} (n) with modulus k and index j.

SumConvergence (Built-in Mathematica Symbol)

SumConvergence[f, n] gives conditions for the sum \[Sum]_n^\[Infinity] f to be convergent.SumConvergence[f, {n_1, n_2, ...}] gives conditions for the multiple sum \[Sum]_n ...

Expectation (Built-in Mathematica Symbol)

Expectation[expr, x \[Distributed] dist] gives the expectation of expr under the assumption that x follows the probability distribution dist. Expectation[expr, x ...

Additive Number Theory (Mathematica Guide)

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

ButcherBeta (Numerical Differential Equation Analysis Package Symbol)

ButcherBeta[tree] gives the number of ways of labeling tree with ButcherOrder[tree] - 1 distinct labels such that the root is not labeled, but every other vertex is labeled. ...