Debye function

In mathematics, the family of Debye functions is defined by

$D_n(x) = \frac{n}{x^n} \int_0^x \frac{t^n}{e^t - 1}\,dt.$

The functions are named in honor of Peter Debye, who came across this function (with n = 3) in 1912 when he analytically computed the heat capacity of a solid. His method is now called the Debye model.

See also

• Incomplete polylogarithm
• Polylogarithm

References

• Abramowitz, Milton; Stegun, Irene A., eds. (1965), "Chapter 27", Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover, pp. 998, ISBN 978-0486612720, MR0167642, http://www.math.sfu.ca/~cbm/aands/page_998.htm .

External links

• Fortran 77 code by Allan MacLeod from Transactions on Mathematical Software
• Fortran 90 version
• "Debye function" entry in MathWorld

This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it.v · Categories: Mathematical analysis stubs Special functions Wikimedia Foundation. 2010. Игры ⚽ Поможем сделать НИР Dawson function Yagan Look at other dictionaries: Debye model — Statistical mechanics Thermodynamics · …   Wikipedia Debye relaxation — is the dielectric relaxation response of an ideal, noninteracting population of dipoles to an alternating external electric field. It is usually expressed in the complex permittivity varepsilon of a medium as a function of the field s frequency… …   Wikipedia Debye–Hückel theory — The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes.[1] It was based on an extremely simplified model of the electrolyte solution but… …   Wikipedia Debye–Hückel equation — The Debye–Hückel equation and Debye–Hückel limiting law, were derived by Peter Debye and Erich Hückel, who developed a theory with which to calculate activity coefficients of electrolyte solutions.[1] Activities, rather than concentrations, are… …   Wikipedia Debye-Hückel equation — The Debye Hückel limiting law, named for its developers Peter Debye and Erich Hückel, provides one way to obtain activity coefficients Ref|Harris. Activities, rather than concentrations, are needed in many chemical calculations because solutions… …   Wikipedia Debye sheath — The Debye sheath (also electrostatic sheath) is a layer in a plasma which has a greater density of positive ions, and hence an overall excess positive charge, that balances an opposite negative charge on the surface of a material with which it is …   Wikipedia Debye–Waller factor — The Debye–Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x ray scattering or coherent neutron scattering caused by thermal motion.[1][2] It has also been called the …   Wikipedia Debye-Waller factor — The Debye Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x ray scattering or neutron scattering caused by thermal motion or quenched disorder. It has also been… …   Wikipedia Peter Debye — Infobox Scientist name = Peter Debye image size= 180px birth date = birth date|1884|3|24|mf=y birth place = Maastricht, Netherlands death date = death date and age|1966|11|2|1884|3|24 death place = Ithaca, New York, USA nationality = Netherlands… …   Wikipedia Bessel function — In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel s differential equation: for an arbitrary real or complex number α (the order of the …   Wikipedia 18+ © Academic, 2000-2025 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”