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§27.7 Lambert Series as Generating Functions►Lambert series have the form …
§4.13 has been enlarged. The Lambert -function is multi-valued and we use the notation , , for the branches. The original two solutions are identified via and .
Other changes are the introduction of the Wright -function and tree -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 , additional Maclaurin series (4.13.5_1) and (4.13.5_2), an explicit expansion about the branch point at 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 -functions in the end of the section.