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WeberE

WeberE[Nu, z]
gives the Weber function E_nu(z).
WeberE[Nu, Mu, z]
gives the associated Weber function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • E_nu(z) satisfies the differential equation z^2y^('')+zy^'+(z^2-nu^2)y=-(z+nu+(z-nu)cos(pi nu))/pi.
  • E_nu(z) is defined by .
  • WeberE[Nu, z] is an entire function of z with no branch cut discontinuities.
  • For certain special arguments, WeberE automatically evaluates to exact values.
  • WeberE can be evaluated to arbitrary numerical precision.
  • WeberE automatically threads over lists.
EXAMPLESCLOSE ALL
Scope   (5)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
WeberE threads element-wise over lists:
TraditionalForm formatting:
Properties & Relations   (1)
Use FunctionExpand to expand WeberE into hypergeometric functions:
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