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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 > Logarithmic cases





http://functions.wolfram.com/03.03.06.0041.01









  


  










Input Form





BesselY[\[Nu], z] == (1/Pi) (-1)^((Abs[\[Nu]] - \[Nu])/2) (2 Log[z/2] (z/2)^Abs[\[Nu]] Sum[((-1)^k/(k! (k + Abs[\[Nu]])!)) (z/2)^(2 k), {k, 0, Infinity}] - Sum[((Abs[\[Nu]] - k - 1)!/k!) (z/2)^(2 k), {k, 0, Abs[\[Nu]] - 1}]/ (z/2)^Abs[\[Nu]] - (z/2)^Abs[\[Nu]] Sum[(((-1)^k (PolyGamma[k + 1] + PolyGamma[k + Abs[\[Nu]] + 1]))/ (k! (k + Abs[\[Nu]])!)) (z/2)^(2 k), {k, 0, Infinity}]) /; Element[\[Nu], Integers]










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