Define S_n(x) | congruent | sum_(k = 1)^∞ (sin(k x))/k^n C_n(x) | congruent | sum_(k = 1)^∞ (cos(k x))/k^n, then the Clausen functions are defined by Cl_n(x) congruent {S_n(x) = sum_(k = 1)^∞ (sin(k x))/k^n | n even C_n(x) = sum_(k = 1)^∞ (cos(k x))/k^n | n odd, auto right match sometimes also written as ψ_n(x).
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