Sentence examples for formulas for f from inspiring English sources

□. Next, we find explicit formulas for f, g and h.

After obtaining the formulas for f (p 0 |   x 0 ) and f (p t |   p 0,   N e ), the integral with respect to p 0 in the likelihood function (Equation 6) can be calculated in advance.

In [4], they obtained some monotonicity formulas for F-stationary maps via the coarea formula and the comparison theorem.

and the corresponding duplication formula for f is f ( 2 x ) = g ( f ( x ) ).

We may not be given a formula for (f(x)) as a function of (x).

A recurrence formula for F n ( x ; λ ; μ ; ν ) is given by the next theorem.

4This value is simply obtained by setting n m = 1 in the formula for f e (footnote 2).

A Lévy-Khinchin-type integral formula for f is then explicitly obtained by solving a difference equation of the form ∑i = 02κaif(n + i) = ∝ xndv.

There is a parallel formula for (f in Sigma _{s}' (mathbf {R}^{d})), (phi in Sigma _{s}(mathbf {R}^{d})) and (s> 1/2), that we also prove.

Since this alternative formula for f j ignores interruptions it would grossly underestimate the finishing dates in general and so we do not discuss it further.

Using the formula for F ( 1, M + 1 ) in Appendix E.2, we obtain that tr ( U T q M i h ) = i 2 L holds for every integer q.