The Anger function - Maple Help

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AngerJ - The Anger function

WeberE - The Weber function

Calling Sequence

AngerJ(v, x)

WeberE(v, x)

Parameters

v

-

algebraic expression (the order or index)

x

-

algebraic expression (the argument)

Description

• 

The Anger function AngerJ(v,x) solves the inhomogeneous Bessel equation

x2y''+xy'+x2v2y=xvsinvππ

• 

The Weber function WeberE(v,x) solves the inhomogeneous Bessel equation

x2y''+xy'+x2v2y=vxcosvπv+xπ

Examples

AngerJ0,0

1

(1)

evalfAngerJ4,3

0.1320341839

(2)

WeberE1.5I,2.6+3I

4.13519769211.77785498I

(3)

seriesAngerJ13,x,x,4

323π+9163πx27703πx28112803πx3+Ox4

(4)

seriesWeberE12,x,x,6

2π+43πx815πx216105πx3+32945πx4+6410395πx5+Ox6

(5)

xAngerJv,x

AngerJv+1,x+vAngerJv,xxsinvππx

(6)

xWeberEv,x

WeberEv+1,x+vWeberEv,xx1cosvππx

(7)

See Also

Airy, Bessel, initialfunctions, Kelvin, Struve

References

  

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.


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