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Find a numerical approximation of a residue of an expression around the specified point
ResourceFunction["NResidue"][expr,{z,z0}] numerically finds the residue of expr near the point z=z0. |
"Radius" | 1/100 | radius of contour on which integral is evaluated |
Method | Trapezoidal | integration method to use |
Residue of the function about the origin:
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NResidue can find residues of functions with essential singularities:
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Since Series is unable to handle essential singularities, Residue returns unevaluated:
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NResidue allows for some error in the location of the pole:
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Due to machine-precision arithmetic, z→1 is not a pole:
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With Residue, the error in the location of the pole yields a result of zero:
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NResidue threads element-wise over lists:
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Use "Radius" to shrink the radius of the contour of integration to isolate a single pole:
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Increase the radius to improve convergence of the integration if no other poles are nearby:
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NResidue accepts options for NIntegrate, which are sometimes necessary to get an accurate result:
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Use NResidue to evaluate derivatives of a function evaluated at a point:
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Residues of numerical functions:
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NSeries can also compute residues of numerical functions:
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Using NSeries:
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NResidue will return an incorrect result when the integration contour contains branch cuts:
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Wolfram Language 11.3 (March 2018) or above
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