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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Series representations > Generalized power series > Expansions of (1+z)a at z==0 > Expansions of (1+Sumk=1infinityck zk)a at z==0





http://functions.wolfram.com/01.02.06.0062.01









  


  








Input Form





(1 + Sum[Subscript[c, k] z^k, {k, 1, Infinity}])^a == a Sum[Binomial[k - a, k] Sum[(((-1)^j Binomial[k, j])/(a - j)) Subscript[p, j, k] z^k, {j, 0, k}], {k, 0, Infinity}] /; Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/k) Sum[(j m - k + m) Subscript[c, m] Subscript[p, j, k - m], {m, 1, k}] && Element[k, Integers] && k > 0 && !(Element[a, Integers] && a > 0)








Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <notin /> <ci> a </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02