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This chapter introduces the Lambert W function and its extended form, the g-function (LogWright function). Historical development, mathematical properties, and practical applications of these functions in engineering and physics are discussed. Both numerical and analytical methods for solving Lambert W and g-function equations are presented, including Newton’s and Halley’s iterative procedures, Taylor series expansions, and the Special Trans Function Theory (STFT). Numerical examples illustrate the accuracy and convergence of these methods.

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Lambert W Function

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  • 发表日期：

    2026年

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  • Martin Ćalasan,
  • Snežana Vujošević

摘要

This chapter introduces the Lambert W function and its extended form, the g-function (LogWright function). Historical development, mathematical properties, and practical applications of these functions in engineering and physics are discussed. Both numerical and analytical methods for solving Lambert W and g-function equations are presented, including Newton’s and Halley’s iterative procedures, Taylor series expansions, and the Special Trans Function Theory (STFT). Numerical examples illustrate the accuracy and convergence of these methods.