Through

Through[p[f1,f2][x]]

gives p[f1[x],f2[x]].

Through[expr,h]

performs the transformation wherever h occurs in the head of expr.

Details

  • Through distributes operators that appear inside the heads of expressions.

Examples

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Basic Examples  (2)

Apply all functions in a list to the same argument:

Apply a sum of functions by forming the sum of the individual applications:

Scope  (2)

By default, the operation is performed for any function in the head:

Perform the operation only if the head is a sum of terms:

Applications  (2)

Apply a differential operator:

Properties & Relations  (2)

Tabulate square roots of values without using auxiliary variables:

Introduced in 1988
 (1.0)