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StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in trigonometric form > Using trigonometric functions with branch cut-containing arguments





http://functions.wolfram.com/03.09.06.0010.01









  


  










Input Form





StruveH[\[Nu], z] \[Proportional] (Sqrt[2/Pi] z^(\[Nu] + 1) (Sin[Sqrt[z^2] - ((2 \[Nu] + 1)/4) Pi] HypergeometricPFQ[{(1 - 2 \[Nu])/4, (3 - 2 \[Nu])/4, (1 + 2 \[Nu])/4, (3 + 2 \[Nu])/4}, {1/2}, -(1/z^2)] + ((4 \[Nu]^2 - 1)/(8 Sqrt[z^2])) Cos[Sqrt[z^2] - ((2 \[Nu] + 1)/4) Pi] HypergeometricPFQ[ {(3 - 2 \[Nu])/4, (5 - 2 \[Nu])/4, (3 + 2 \[Nu])/4, (5 + 2 \[Nu])/4}, {3/2}, -(1/z^2)]))/(z^2)^((3 + 2 \[Nu])/4) + ((2^(1 - \[Nu]) z^(\[Nu] - 1))/(Sqrt[Pi] Gamma[1/2 + \[Nu]])) HypergeometricPFQ[{1/2, 1/2 - \[Nu], 1}, {}, -(4/z^2)] /; (Abs[z] -> Infinity)










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 1 </cn> </list> <list /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Rule </ci> <apply> <abs /> <ci> z </ci> </apply> <infinity /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.