AngerJ
The Anger function
WeberE
The Weber function
Calling Sequence
Parameters
Description
Examples
References
AngerJ(v, x)
WeberE(v, x)
v
-
algebraic expression (the order or index)
x
algebraic expression (the argument)
The Anger function AngerJ(v,x) solves the inhomogeneous Bessel equation
x2⁢y''+x⁢y'+x2−v2⁢y=x−v⁢sin⁡v⁢ππ
The Weber function WeberE(v,x) solves the inhomogeneous Bessel equation
x2⁢y''+x⁢y'+x2−v2⁢y=v−x⁢cos⁡v⁢π−v+xπ
AngerJ⁡0,0
1
evalf⁡AngerJ⁡4,3
0.1320341839
WeberE⁡1.5−I,2.6+3⁢I
4.135197692−11.77785498⁢I
series⁡AngerJ⁡13,x,x,4
3⁢32⁢π+916⁢3π⁢x−2770⁢3π⁢x2−811280⁢3π⁢x3+O⁡x4
series⁡WeberE⁡12,x,x,6
2π+43⁢1π⁢x−815⁢1π⁢x2−16105⁢1π⁢x3+32945⁢1π⁢x4+6410395⁢1π⁢x5+O⁡x6
∂∂x⁢AngerJ⁡v,x
−AngerJ⁡v+1,x+v⁢AngerJ⁡v,xx−sin⁡v⁢ππ⁢x
∂∂x⁢WeberE⁡v,x
−WeberE⁡v+1,x+v⁢WeberE⁡v,xx−1−cos⁡v⁢ππ⁢x
Abramowitz, M., and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.
Watson, G.N. A Treatise on the Theory of Bessel Functions. Cambridge University Press, 1966.
See Also
Airy
Bessel
initialfunctions
Kelvin
Struve
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