# Vocabulary/tco

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`u t: y`Weighted Taylor Adverb

Rank 0 *-- operates on individual atoms of y, producing a result of the same shape --*
WHY IS THIS IMPORTANT?

The `y`-th coefficient(s) in the Taylor series that approximates the function (`u`), multiplied by (`!y`).

(`u t: y`) differs from (`u t. y`) by being *weighted* by the *factorial term(s)* (`!y`)

i=: i.8 u=: ^ NB. sample u: the exponential function u t: i 1 1 1 1 1 1 1 1

### Common Uses

Use `t:` in place of `t.` to simplify the appearance of the resulting series of coefficients and reveal a hidden pattern.
This works because many common Taylor expansions have coefficients with factorial terms in the denominator.

u t: i 1 1 1 1 1 1 1 1 u t. i NB. compare t. with t: 1 1 0.5 0.166667 0.0416667 0.00833333 0.00138889 0.000198413

See Taylor Coefficient (`t.`) where this same example is discussed in greater depth.

### Related Primitives

Taylor Coefficient (`t.`), Taylor Approximation (`T.`)