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Everything about Clausen function
Transcendental single-variable function
In mathematics, the Clausen function, introduced by Thomas Clausen, is a transcendental, special function of a single variable. It can be expressed in the form of a definite integral, a trigonometric series, and various other forms. It is intimately connected with the polylogarithm, inverse tangent integral, polygamma function, Riemann zeta function, Dirichlet eta function, and Dirichlet beta function. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Clausen functionA 5-minute orientation
- Skim a recent paper: Quadrature processes for efficient calculation of the Clausen functionsInfluential work since 2022
- Pick up a classic book: Textbook of drug design and discoveryThe most-reprinted book on the subject
- Read the landmark paper: Chebyshev coefficients for the Clausen function Cl2(x)Cited 6 times
- Go sideways: Hurwitz zeta functionA closely related topic
- Go sideways: List of mathematical seriesA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
- Basic properties
- General definition
- Relation to the Bernoulli polynomials
- Duplication formula
- Derivatives of general-order Clausen functions
- Relation to the inverse tangent integral
- Relation to the Barnes' G-function
- Relation to the polylogarithm
- Relation to the polygamma function
- Relation to the generalized logsine integral
- Kummer's relation
- Relation to the Lobachevsky function
🏆 Landmark papers (most cited)
Chebyshev coefficients for the Clausen function Cl2(x)
On the closed form of Clausen functions
Three-level models solvable in terms of the Clausen function
Some hypergeometric transformations and reduction formulas for the Gauss function and their applications involving the Clausen function
Pulmonary Function Testing Guidelines and Controversies Jack L. Clausen, ed. New York
Jack L. Clausen, Editor (1st edition), Pulmonary Function Testing Guidelines and Controversies, Academic Press, Springfield (1982).
🆕 Influential since 2022
📚 Books worth reading
Textbook of drug design and discoveryUlf Madsen, Povl Krogsgaard-Larsen · 2009
The Conspirators HierarchyJohn Coleman · 1992
Pulmonary function testing, guidelines and controversiesJack Clausen · 1982- 📕Complex carbohydrates in drug researchAlfred Benzon Symposium (36th 1993 Royal Danish Academy of Sciences and Letters) · 1994
Euler at 300Robert E. Bradley · 2007- 📕MicrogliaBertrand Joseph, José Luis Venero · 2013
- 📕Pulmonary function testing guidelines and controversiesClausen · 1984
- 📕Pulmonary Function Testing Guidelines and ControversiesJack Clausen · 1984
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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