Difference between revisions of "Weber function"
From specialfunctionswiki
| (7 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
The Weber function is defined by | The Weber function is defined by | ||
| − | $$\mathbf{E}_{\nu}(z)=\dfrac{1}{\pi} \displaystyle\int_0^{\pi} \sin(\nu \theta - z \sin(\theta))d\theta.$$ | + | $$\mathbf{E}_{\nu}(z)=\dfrac{1}{\pi} \displaystyle\int_0^{\pi} \sin(\nu \theta - z \sin(\theta)) \mathrm{d}\theta.$$ |
=Properties= | =Properties= | ||
| − | + | [[Relationship between Weber function and Anger function]]<br /> | |
| − | + | [[Relationship between Anger function and Weber function]]<br /> | |
| − | + | [[Relationship between Weber function 0 and Struve function 0]]<br /> | |
| + | [[Relationship between Weber function 1 and Struve function 1]]<br /> | ||
| + | [[Relationship between Weber function 2 and Struve function 2]]<br /> | ||
=References= | =References= | ||
| − | + | * {{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 | |
| + | |||
| + | [[Category:SpecialFunction]] | ||
| + | [[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
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 12.3.3
