Difference between revisions of "Weber function"

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The Weber function is defined by
 
The Weber function is defined by
$$\mathbf{E}_{\nu}(z)=\dfrac{1}{\pi} \displaystyle\int_0^{\pi} \sin(\nu \theta - z \sin(\theta))d\theta.$$
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$$\mathbf{E}_{\nu}(z)=\dfrac{1}{\pi} \displaystyle\int_0^{\pi} \sin(\nu \theta - z \sin(\theta)) \mathrm{d}\theta.$$
  
 
=Properties=
 
=Properties=
{{:Relationship between Weber function and Anger function}}
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[[Relationship between Weber function and Anger function]]<br />
{{:Relationship between Anger function and Weber function}}
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[[Relationship between Anger function and Weber function]]<br />
 +
[[Relationship between Weber function 0 and Struve function 0]]<br />
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[[Relationship between Weber function 1 and Struve function 1]]<br />
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[[Relationship between Weber function 2 and Struve function 2]]<br />
  
 
=References=
 
=References=
[http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_498.htm Abramowitz and Stegun]
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Anger of integer order is Bessel J|next=Relationship between Anger function and Weber function}}: 12.3.3
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[[Category:SpecialFunction]]
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[[Category:Definition]]

Latest revision as of 04:13, 6 June 2016

The Weber function is defined by $$\mathbf{E}_{\nu}(z)=\dfrac{1}{\pi} \displaystyle\int_0^{\pi} \sin(\nu \theta - z \sin(\theta)) \mathrm{d}\theta.$$

Properties

Relationship between Weber function and Anger function
Relationship between Anger function and Weber function
Relationship between Weber function 0 and Struve function 0
Relationship between Weber function 1 and Struve function 1
Relationship between Weber function 2 and Struve function 2

References