WebMedia in category "Polylogarithm" The following 21 files are in this category, out of 21 total. Webpolylogarithms translation in German - English Reverso dictionary, see also 'polygam',Polygamie',polymorph',Polarlicht', examples, definition, conjugation
Traducere
WebIn mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li s (z) of order s and argument z.Only for special values of s does … WebMultiplikationssatz -. Multiplication theorem. In der Mathematik ist das Multiplikationstheorem eine bestimmte Art von Identität, der viele spezielle Funktionen im … side of the house greenhouse
Bochner
WebTranslate Polylogarithmus. See Spanish-English translations with audio pronunciations, examples, and word-by-word explanations. In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the … See more In the case where the order $${\displaystyle s}$$ is an integer, it will be represented by $${\displaystyle s=n}$$ (or $${\displaystyle s=-n}$$ when negative). It is often convenient to define Depending on the … See more • For z = 1, the polylogarithm reduces to the Riemann zeta function Li s ( 1 ) = ζ ( s ) ( Re ( s ) > 1 ) . {\displaystyle \operatorname {Li} _{s}(1)=\zeta (s)\qquad (\operatorname {Re} (s)>1).} • The polylogarithm is related to Dirichlet eta function and … See more For z ≫ 1, the polylogarithm can be expanded into asymptotic series in terms of ln(−z): where B2k are the Bernoulli numbers. Both versions hold for all s and for any arg(z). As usual, the summation should be terminated when the … See more For particular cases, the polylogarithm may be expressed in terms of other functions (see below). Particular values for the … See more Any of the following integral representations furnishes the analytic continuation of the polylogarithm beyond the circle of … See more 1. As noted under integral representations above, the Bose–Einstein integral representation of the polylogarithm may be extended to … See more The dilogarithm is the polylogarithm of order s = 2. An alternate integral expression of the dilogarithm for arbitrary complex argument z is (Abramowitz & Stegun 1972, § 27.7): See more Webnoun A function of complex numbers related to logarithms See Also: dilogarithm, trilogarithm side of the heart