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Useful Formulae

Riemanns zeta function Probably the most challenging and mysterious object of modern mathematics,in spite of its utter simplicity M.C.Gutzwiller x 1 x1 where pkis the kth prime number. 1 2x 1 Tan formul if t tan, sin cos tan Maclaurin expansion fx f0 xf0 f0 f0 4 arscin x x 4 7 6 5 4 3 , , , 58 expansions extras 2 1 1t2 Fractions ex 1 x so e 1 1 log1x x 1x 1 2 x2 3 x3 2x 2 1 x x2 x3 x4 1x1 1 x radians sin x x , cos x 1 x in radians 2 1 11 1t2 2t 1t2 1t2 2t ba bd adbc bd ac 2x 1 k 1 1 3 1 4 x4 4 1 3x 3 4x 4 31 51 71 91 3 x3 5 x5 7 x7 2 x2 4 x4 6 x6 21x 3 21 x 5 3 21 x 7 3 5 1 Taylor expansion fx fxa afxa fxa fxa 2 a2 3 a3 2 x2 3 x3 dc ba dc bd adbc ba dc bc ad ba dc 2 1 3x 1 4x 1 3x 1 1 1 5x 1 1 1 px 1 1
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