Function Repository Resource:

AngerWeberA

Evaluate the associated Anger–Weber function

Contributed by: Jan Mangaldan
 ResourceFunction["AngerWeberA"][ν,z] gives the associated Anger–Weber function .

Details

Mathematical function, suitable for both symbolic and numerical manipulation.
is defined by .
ResourceFunction["AngerWeberA"][ν,z] has a branch cut discontinuity in the complex z plane running from - to 0.
For certain special arguments, ResourceFunction["AngerWeberA"] automatically evaluates to exact values.
ResourceFunction["AngerWeberA"] can be evaluated to arbitrary numerical precision.

Examples

Basic Examples (2)

Evaluate numerically:

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Plot :

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Scope (4)

Evaluate for complex arguments:

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Evaluate to arbitrary precision:

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The precision of the output tracks the precision of the input:

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Simple exact values are generated automatically:

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Properties and Relations (7)

Use FunctionExpand to expand AngerWeberA into hypergeometric functions:

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Compare AngerWeberA with the integral definition:

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Express AngerWeberA in terms of the Lommel function LommelS:

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Verify a differential equation for AngerWeberA:

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Verify a recurrence identity for AngerWeberA:

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An identity relating AngerWeberA and AngerJ:

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An identity relating AngerWeberA and WeberE:

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Version History

• 1.1.0 – 14 September 2021