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StruveL






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveL[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in trigonometric and hyperbolic forms > Using hyperbolic functions with branch cut-free arguments





http://functions.wolfram.com/03.10.06.0067.01









  


  










Input Form





StruveL[\[Nu], z] \[Proportional] (Sqrt[2/Pi] z^(\[Nu] + 1) ((-(Sin[((2 \[Nu] + 1)/4) Pi] Cosh[z] + (z/Sqrt[-z^2]) Cos[((2 \[Nu] + 1)/4) Pi] Sinh[z])) (Sum[((Pochhammer[(1 - 2 \[Nu])/4, k] Pochhammer[(3 - 2 \[Nu])/4, k] Pochhammer[(1 + 2 \[Nu])/4, k] Pochhammer[(3 + 2 \[Nu])/4, k])/ (Pochhammer[1/2, k] k!)) (1/z^2)^k, {k, 0, n}] + O[1/z^(2 n + 2)]) + ((4 \[Nu]^2 - 1)/8) ((1/Sqrt[-z^2]) Cos[((2 \[Nu] + 1)/4) Pi] Cosh[z] + (1/z) Sin[((2 \[Nu] + 1)/4) Pi] Sinh[z]) (Sum[((Pochhammer[(3 - 2 \[Nu])/4, k] Pochhammer[(5 - 2 \[Nu])/4, k] Pochhammer[(3 + 2 \[Nu])/4, k] Pochhammer[(5 + 2 \[Nu])/4, k])/ (Pochhammer[3/2, k] k!)) (1/z^2)^k, {k, 0, n}] + O[1/z^(2 n + 2)])))/(-z^2)^((3 + 2 \[Nu])/4) - ((2^(1 - \[Nu]) z^(\[Nu] - 1))/(Sqrt[Pi] Gamma[1/2 + \[Nu]])) (Sum[Pochhammer[1/2, k] Pochhammer[1/2 - \[Nu], k] (4/z^2)^k, {k, 0, n}] + O[1/z^(2 n + 2)]) /; (Abs[z] -> Infinity)










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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