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polylog
In mathematics, the polylogarithm (also known as Jonquière's function) is a special function Li_s(z) that 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.
Computes the usual polylogarithm with the index s at the argument z. For s = 2 the polylogarithm is the dilogarithm, called Spence function. The argument z = 1 represents the special case of the Riemann Zeta function. A more general case is the Nielson generalized polylogarithm, which can be used with more argument p.
Argument s
Scalar
Argument z
Scalar
Returns 1. entry
Scalar
polylog(1, 0.3)
Evaluates the polylogarithm for s = 1 and z = 0.3.
Computes the usual polylogarithm with the index s for every value of the matrix Z.
Argument s
Scalar
Argument Z
Matrix
Returns 1. entry
Matrix
polylog(1, [0.1 0.3 0.5 1.0])
Evaluates the polylogarithm for s = 1 at z = 0.1, z = 0.3, z = 0.5 and z = 1.0.
A generalization of the polylogarithm function. The function reduces to the usual polylogarithm for the case n -> n-1 and p = 1. Therefore S_(n - 1, 1)(z) = Li_n(z).
Argument n
Scalar
Argument p
Scalar
Argument z
Scalar
Returns 1. entry
Scalar
polylog(1, 2, 0.5)
Evaluates the Nielson generalized polylogarithm at n = 1, p = 2 and z = 0.5. For p = 1 we have the ordinary polylogarithm.