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## Lambert $W$-Function Branch Identities

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#### Abstract

After defining in detail the Lambert $W$-function branches, we give a large number of exact identities involving (infinite) symmetric functions of these branches, as well as geometrically convergent series for all the branches. In doing so, we introduce a family of polynomials which may be of independent interest.

### Dates and versions

hal-03087491 , version 1 (23-12-2020)

### Identifiers

• HAL Id : hal-03087491 , version 1
• ARXIV :

### Cite

Henri Cohen. Lambert $W$-Function Branch Identities. 2020. ⟨hal-03087491⟩

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