Weber function

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): 12.3.3