Thomas Clausen (1801–1885) was a Danish mathematician, astronomer, and geophysicist who introduced the functions , defined in terms of polylogarithms [1]; 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 [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].

[6] J. Wu, X. Zhang, and D. Liu, "An Efficient Calculation of the Clausen Functions ," BIT Numerical Mathematics, 50(1), 2010 pp. 193–206. doi:10.1007/s10543-009-0246-8.