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Clausen Functions

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Thomas Clausen (1801–1885) was a Danish mathematician, astronomer, and geophysicist who introduced the functions
Cl
n
(x)
, defined in terms of polylogarithms [1]; the case
Cl
2
(x)
is called Clausen's integral. These functions are useful to define because some identities connect them with the Barnes
G
function, polylogarithm and polygamma functions, and Dirichlet
L
functions [2]. They can also be used to evaluate some divergent Fourier series [3] and in the computation of singular integrals in quantum field theory [4]. For complex arguments, they are related to zeta functions. Efficient methods to calculate Clausen functions can be found in [5, 6].
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