Spence's function
Encyclopedia
In mathematics
, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm. Lobachevsky's function and Clausen's function are closely related functions. Two related special functions
are referred to as Spence's function, the dilogarithm itself, and its reflection with the variable negated:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm. Lobachevsky's function and Clausen's function are closely related functions. Two related special functions
Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
are referred to as Spence's function, the dilogarithm itself, and its reflection with the variable negated:
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William Spence, after whom the function was named by early writers in the field, was a Scottish mathematician working in the early nineteenth century. He was at school with John Galt, who later wrote a biographical essay on Spence.
Identities
Special values
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