§4.13 has been enlarged. The Lambert $W$ -function is multi-valued and we use the notation $W_{k}\left(x\right)$ , $k\in\mathbb{Z}$ , for the branches. The original two solutions are identified via $\operatorname{Wp}\left(x\right)=W_{0}\left(x\right)$ and $\operatorname{Wm}\left(x\right)=W_{\pm 1}\left(x\mp 0\mathrm{i}\right)$ .

Other changes are the introduction of the Wright $\omega$ -function and tree $T$ -function in (4.13.1_2) and (4.13.1_3), simplification formulas (4.13.3_1) and (4.13.3_2), explicit representation (4.13.4_1) for $\frac{{\mathrm{d}}^{n}W}{{\mathrm{d}z}^{n}}$ , additional Maclaurin series (4.13.5_1) and (4.13.5_2), an explicit expansion about the branch point at $z=-{\mathrm{e}}^{-1}$ in (4.13.9_1), extending the number of terms in asymptotic expansions (4.13.10) and (4.13.11), and including several integrals and integral representations for Lambert $W$ -functions in the end of the section.

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explicit representations

1—10 of 15 matching pages

1: 18.5 Explicit Representations

§18.5 Explicit Representations

Chebyshev

2: 16.11 Asymptotic Expansions

3: 26.13 Permutations: Cycle Notation

4: 18.20 Hahn Class: Explicit Representations

§18.20 Hahn Class: Explicit Representations

5: 4.13 Lambert W -Function

6: Bibliography T

7: 18.37 Classical OP’s in Two or More Variables

Explicit Representation

8: 14.30 Spherical and Spheroidal Harmonics

Explicit Representation

9: 18.35 Pollaczek Polynomials

10: Errata

5: 4.13 Lambert $W$ -Function