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