Complex Trilogarithm

版本 1.0.1 (2.3 KB) 作者: Didier Clamond
= Spence's tri-Logarithm.
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更新时间 2023/9/7

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function t = trilog(z)
trilog = Spence's tri-Logarithm.
t = trilog(z) = Li_3(z)
= Sum From n=1 To n=Infinity Of z^n/n^3 if |z|<=1.
INPUT z: real or complex, scalar, vector or matrix.
OUTPUT t: component-wise trilogarithm of z (accuracy around machine precision).
Depending on the size of the matrix z and of the magnitude of its
components, trilog(z) is 2 to 5 (and more) orders of magnitude
faster than the polylog(3,z) from the Matlab symbolic toolbox.
EXAMPLE: trilog(z) vs polylog(3,z).
N = 10000;
z = 200*( rand(N) + i*rand(N) ) - 100 - i*100;
tic; t=trilog(z); toc;
Elapsed time is 12.081650 seconds.
N = 160;
z = 200*( rand(N) + i*rand(N) ) - 100 - i*100;
tic; t=polylog(3,z); toc;
Elapsed time is 12.289606 seconds.

引用格式

Didier Clamond (2024). Complex Trilogarithm (https://www.mathworks.com/matlabcentral/fileexchange/134986-complex-trilogarithm), MATLAB Central File Exchange. 检索来源 .

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