D. Knuth

activity

19922004

most citedDancing links

185 citations · 371 across the 28 of their papers we have counts for

collaborators

Showing math.CAShow all

4 papers · 1 filter

math.CA1995

On the inversion of $y^{α} e^{y}$ in terms of associated Stirling numbers

David J. Jeffrey, Robert M. Corless, David E. G. Hare +1

The function $y = Φ_{α} (x)$ , the solution of $y^{α} e^{y} = x$ for $x$ and $y$ large enough, has a series expansion in terms of $ln x$ and $ln ln x$ , with coefficients given in terms of Sti…

math.CA1994★ 3 cited

Bracket notation for the `coefficient of' operator

Donald E. Knuth

When $G (z)$ is a power series in $z$ , many authors now write ` $[z^{n}] G (z)$ ' for the coefficient of $z^{n}$ in $G (z)$ , using a notation introduced by Goulden and Jackson in [\GJ, p. 1…

math.CA1992★ 109 cited

Johann Faulhaber and sums of powers

Donald E. Knuth

Early 17th-century mathematical publications of Johann Faulhaber contain some remarkable theorems, such as the fact that the $r$ -fold summation of $1^{m}, 2^{m}, ..., n^{m}$ is a polynomial…

math.CA1992★ 54 cited

Convolution polynomials

Donald E. Knuth

The polynomials that arise as coefficients when a power series is raised to the power $x$ include many important special cases, which have surprising properties that are not widely…

On the inversion of yαey in terms of associated Stirling numbers

Bracket notation for the `coefficient of' operator

Johann Faulhaber and sums of powers

Convolution polynomials

On the inversion of $y^{α} e^{y}$ in terms of associated Stirling numbers