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variants of this functions
Log






Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Series representations > Generalized power series > Expansions at generic point z==z0 > Expansions of log(f(z)) at z==z0





http://functions.wolfram.com/01.04.06.0020.01









  


  










Input Form





Log[f[z]] == 2 I Pi Floor[(Pi - Arg[f[Subscript[z, 0]]] - Arg[f[z]/f[Subscript[z, 0]]])/(2 Pi)] + Log[f[Subscript[z, 0]]] + Sum[(((-1)^k (Derivative[1][f][Subscript[z, 0]]/f[Subscript[z, 0]])^ (k + 1))/(k + 1)) Subscript[p, k + 1, s - k] (z - Subscript[z, 0])^(s + 1), {s, 0, Infinity}, {k, 0, s}] /; f[Subscript[z, 0]] != 0 && Derivative[1][f][Subscript[z, 0]] != 0 && Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/(Derivative[1][f][Subscript[z, 0]] k)) Sum[((j m - k + m)/(m + 1)!) Derivative[m + 1][f][Subscript[z, 0]] Subscript[p, j, k - m], {m, 1, k}] && Element[k, Integers] && k > 0










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





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