Everything about Complex logarithm
Logarithm of a complex number
In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related:A complex logarithm of a nonzero complex number, defined to be any complex number for which. Such a number is denoted by. If is given in polar form as, where and are real numbers with, then is one logarithm of, and all the complex logarithms of are exactly the numbers of the form for integers. These logarithms are equally spaced along a vertical line in the complex plane. A complex-valued function, defined on some subset of the set of nonzero complex numbers, satisfying for all in. Such complex logarithm functions are analogous to the real logarithm function, which is the inverse of the real exponential function and hence satisfies eln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of, or by the process of analytic continuation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Complex logarithmA 5-minute orientation
- Pick up a classic book: Ten-decimal tables of the logarithms of complex numbers and for the transformation from Cartesian to polar coordinatesThe most-reprinted book on the subject
- Read the landmark paper: Logarithm of odds (lods) for linkage in complex inheritance.Cited 47 times
- Go sideways: Branch pointA closely related topic
- Go sideways: Multivalued functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Logarithm of odds (lods) for linkage in complex inheritance.
The double logarithm and Manin’s complex for modular curves
Multiscale illumination normalization for face recognition using dual-tree complex wavelet transform in logarithm domain
Low-Complexity High-Precision Method and Architecture for Computing the Logarithm of Complex Numbers
On the complexity of computing the logarithm and square root functions on a complex domain
Computation of the logarithm of Bessel functions of complex argument
Illumination invariant face recognition using dual-tree complex wavelet transform in logarithm domain
Logarithm of a Non-Singular Complex Matrix via the Dunford–Taylor Integral
📚 Books worth reading
- 📕Ten-decimal tables of the logarithms of complex numbers and for the transformation from Cartesian to polar coordinatesL. A. Li︠u︡sternik, Institut tochnoĭ mekhaniki i vychislitel ̕noi tekhniki AN SSSR · 1965
- 📕Ten-decimal tables of the logarithms of complex numbers and for the transformation from Cartesian to polar coordinatesInstitut tochnoi mekhaniki i vychislitel £noi tekhniki AN SSSR. · 1965
- 📕Ten-decimal tables of the logarithms of complex numbers and for the transformation from Cartesian to polar coordinatesAkademiia nauk SSSR. Institut tochnoǐ mekhaniki i vychislitel'noǐ tekhniki · 1965
- 📕Imaginary logarithms ..Leonhard Euler · 1978
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Branch point In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n-valued (has n values)…
- Multivalued function In mathematics, a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in…
- Analytic function In mathematical analysis, an analytic function is a function that is locally represented by a convergent power series. More precisely, a real or complex…
- Inverse trigonometric functions In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions…
- Principal value In mathematics, specifically complex analysis, a multivalued function has often the property that, near almost every point, the graph of the function is…
- Complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that studies complex-valued…
- Holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood…
- Complex plane In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called…