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Power






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.02.06.0036.01









  


  










Input Form





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