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BesselY






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselY[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/03.03.06.0036.01









  


  










Input Form





BesselY[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, m][z, \[Nu]] == Csc[Pi \[Nu]] (Cos[\[Nu] Pi] Sum[((-1)^k (z/2)^(2 k + \[Nu]))/(Gamma[k + \[Nu] + 1] k!), {k, 0, m}] - Sum[((-1)^k (z/2)^(2 k - \[Nu]))/ (Gamma[k - \[Nu] + 1] k!), {k, 0, m}]) == BesselY[\[Nu], z] - ((Csc[Pi \[Nu]] (-1)^m)/(m + 1)!) (((2^(-2 - 2 m + \[Nu]) z^(2 - \[Nu] + 2 m))/Gamma[2 + m - \[Nu]]) HypergeometricPFQ[{1}, {2 + m, 2 + m - \[Nu]}, -(z^2/4)] - ((2^(-2 - 2 m - \[Nu]) z^(2 + \[Nu] + 2 m) Cos[Pi \[Nu]])/ Gamma[2 + m + \[Nu]]) HypergeometricPFQ[{1}, {2 + m, 2 + m + \[Nu]}, -(z^2/4)]) && Element[m, Integers] && m >= 0 /; !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <apply> <notin /> <ci> &#957; </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





© 1998- Wolfram Research, Inc.