Definitions for polylogarithm
po·ly·log·a·rithm

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1. polylogarithmnoun

   A function of complex numbers related to logarithms.

WikipediaRate this definition:0.0 / 0 votes

1. Polylogarithm

   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 polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the Bose–Einstein integral. In quantum electrodynamics, polylogarithms of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams. The polylogarithm function is equivalent to the Hurwitz zeta function — either function can be expressed in terms of the other — and both functions are special cases of the Lerch transcendent. Polylogarithms should not be confused with polylogarithmic functions nor with the offset logarithmic integral which has the same notation, but with one variable. Different polylogarithm functions in the complex plane The polylogarithm function is defined by a power series in z, which is also a Dirichlet series in s:

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1. Polylogarithm

   In mathematics, the polylogarithm is a special function Lis. The polylogarithm is found in the closed form of the integral of the Fermi–Dirac distribution and the Bose–Einstein distribution and is sometimes known as the Fermi–Dirac integral or the Bose–Einstein integral. Polylogarithms should not be confused with polylogarithmic functions nor with the offset logarithmic integral which has a similar notation. The polylogarithm is defined by the infinite sum, or power series: Only for special values of the order s does the polylogarithm reduce to an elementary function such as the logarithm function. The above definition is valid for all complex orders s and for all complex arguments z with |z| < 1; it can be extended to |z| ≥ 1 by the process of analytic continuation. The special case s = 1 involves the ordinary natural logarithm, Li1 = −ln, while the special cases s = 2 and s = 3 are called the dilogarithm and trilogarithm respectively. The name of the function comes from the fact that it may also be defined as the repeated integral of itself: thus the dilogarithm is an integral of the logarithm, and so on. For nonpositive integer orders s, the polylogarithm is a rational function.

Anagrams for polylogarithm »

1. polyalgorithm

How to pronounce polylogarithm?

1. Alex

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How to say polylogarithm in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of polylogarithm in Chaldean Numerology is: 4

2. Pythagorean Numerology

   The numerical value of polylogarithm in Pythagorean Numerology is: 9

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Polylogarithm
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Polylogarithm
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=polylogarithm