Pole

A Complex function has a pole of order at if, in the Laurent Series, for and . Equivalently, has a pole of order at if is the smallest Positive Integerfor which is differentiable at . If , there is no pole at .Otherwise, the order of the pole is the greatest Positive Coefficient in the Laurent Series.

This is equivalent to finding the smallest such that

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 396-397, 1985.

• Fundamental Continuity Theorem
• Fundamental Discriminant
• Fundamental Forms
• Fundamental Group
• Fundamental Homology Class
• Fundamental Lemma of Calculus of Variations
• Fundamental System
• Fundamental Theorem of Algebra
• Fundamental Theorem of Arithmetic
• Fundamental Theorem of Curves
• Fundamental Theorem of Directly Similar Figures
• Fundamental Theorem of Gaussian Quadrature
• Fundamental Theorem of Genera
• Fundamental Theorem of Plane Curves
• Fundamental Theorem of Projective Geometry
• Fundamental Theorem of Space Curves
• Fundamental Theorem of Symmetric Functions
• Fundamental Theorems of Calculus
• Fundamental Unit
• Funnel
• Fuss's Problem
• Futile Game
• Fuzzy Logic
• FWHM
• Gabriel's Horn