KnowraComplex logarithmLinked fromLinked fromThe 17 pages that link to Complex logarithm, each with the reason it gives.All 17Broader topic 5Related 10Compared with 2LogarithmBroader topic: Extending logarithms beyond positive reals introduces branches and multiple possible values.Analytic continuationBroader topic: Continuing a local logarithm around zero can return a different value.Euler's formulaRelated: Earlier logarithmic relations helped frame the connection Euler expressed exponentially.Complex exponentialCompared with: Its multiple branches arise because the exponential repeats every 2πi.Natural logarithmCompared with: Unlike the real natural logarithm, its complex extension is multivalued unless a branch is chosen.Winding numberRelated: A continuous logarithm along a closed curve accumulates 2πi times its winding number.Inverse trigonometric functionsRelated: Complex inverse trigonometric functions can be expressed using logarithms.Complex modulusRelated: The modulus determines the real component of each logarithm value.Branch pointBroader topic: A loop around zero adds 2πi, producing infinitely many branches.Complex derivativeBroader topic: Each branch is complex-differentiable on its domain, illustrating the role of domain choice.Polar formRelated: Its angle choices expose the multiple representations created by full rotations.Binary logarithmBroader topic: It extends log₂ beyond positive real inputs, where values become multivalued.Hadamard three-circle theoremRelated: The theorem uses the real logarithms of radii and moduli, not a complex logarithm branch.Lambert W functionRelated: Its multivaluedness helps explain why Lambert W has infinitely many complex branches.Logarithmic differentiationRelated: Complex logarithms introduce branch choices absent from the usual positive-real method.Inverse hyperbolic functionsRelated: Complex inverse hyperbolic functions inherit logarithmic branch choices and their discontinuities.Exponential integralRelated: The logarithmic term governs the local behavior and branches of Ei near zero.
KnowraComplex logarithmLinked fromLinked fromThe 17 pages that link to Complex logarithm, each with the reason it gives.All 17Broader topic 5Related 10Compared with 2LogarithmBroader topic: Extending logarithms beyond positive reals introduces branches and multiple possible values.Analytic continuationBroader topic: Continuing a local logarithm around zero can return a different value.Euler's formulaRelated: Earlier logarithmic relations helped frame the connection Euler expressed exponentially.Complex exponentialCompared with: Its multiple branches arise because the exponential repeats every 2πi.Natural logarithmCompared with: Unlike the real natural logarithm, its complex extension is multivalued unless a branch is chosen.Winding numberRelated: A continuous logarithm along a closed curve accumulates 2πi times its winding number.Inverse trigonometric functionsRelated: Complex inverse trigonometric functions can be expressed using logarithms.Complex modulusRelated: The modulus determines the real component of each logarithm value.Branch pointBroader topic: A loop around zero adds 2πi, producing infinitely many branches.Complex derivativeBroader topic: Each branch is complex-differentiable on its domain, illustrating the role of domain choice.Polar formRelated: Its angle choices expose the multiple representations created by full rotations.Binary logarithmBroader topic: It extends log₂ beyond positive real inputs, where values become multivalued.Hadamard three-circle theoremRelated: The theorem uses the real logarithms of radii and moduli, not a complex logarithm branch.Lambert W functionRelated: Its multivaluedness helps explain why Lambert W has infinitely many complex branches.Logarithmic differentiationRelated: Complex logarithms introduce branch choices absent from the usual positive-real method.Inverse hyperbolic functionsRelated: Complex inverse hyperbolic functions inherit logarithmic branch choices and their discontinuities.Exponential integralRelated: The logarithmic term governs the local behavior and branches of Ei near zero.