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Everything about Bessel function
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena with circular or cylindrical symmetry. They are named after the German astronomer and mathematician Friedrich Bessel, who studied them systematically in 1824. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Bessel functionA 5-minute orientation
- Skim a recent paper: Normalized generalized Bessel function and its geometric propertiesInfluential work since 2022
- Pick up a classic book: A treatise on the theory of Bessel functionsThe most-reprinted book on the subject
- Read the landmark paper: A BESSEL FUNCTION DISTRIBUTIONCited 80 times
- Go sideways: Anger functionA closely related topic
- Go sideways: Struve functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A BESSEL FUNCTION DISTRIBUTION
The q-j Bessel Function
Bessel Function Approximations
A generalized Bessel function
Automatic computation of Bessel function integrals
Methods for incomplete Bessel function evaluation
Bessel function model of corneal topography
Zeros of Bessel function derivatives
🆕 Influential since 2022
Normalized generalized Bessel function and its geometric properties
The Hartley–Bessel function: product formula and convolution structure
Identities associated to a generalized divisor function and modified Bessel function
Bessel equation and Bessel function on $\mathbb{T}_{(q,h)}$
Analytical and geometrical approach to the generalized Bessel function
📚 Books worth reading
A treatise on the theory of Bessel functionsG. N. Watson · 1922
Bessel functions and their applicationsB. G. Korenev · 2002- 📕Tables of the Bessel functions of the first kind of ordersHarvard University. Computation Laboratory · 1947
Studien über die bessel'schen FunctionenEugene Lommel · 1868
A treatise on Bessel functions and their applications to physicsAndrew Gray · 1895
Einleitung in die Theorie der Bessel'schen FunktionenJ. H. Graf · 1898
Integrals of Bessel functionsYudell L. Luke · 1962
Solved problems in analysisOrin J. Farrell, Bertram Ross · 1971
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Anger function In mathematics, the Anger function, introduced by C. T. Anger (1855), is a function defined as 𝐉ν(z)=1π∫0πcos(νθ−zsinθ)dθ with complex parameter ν and…
- Struve function In mathematics, the Struve functions Hα(x), are solutions y(x) of the non-homogeneous Bessel's differential equation: x2d2ydx2+xdydx+(x2−α2)y=4(x2)α+1πΓ(α+12)…
- Parabolic cylinder function In mathematics, the parabolic cylinder functions are special functions defined as solutions to the differential equation This equation is found when the…
- Hankel transform In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind…
- Bessel–Clifford function In mathematical analysis, the Bessel–Clifford function, named after Friedrich Bessel and William Kingdon Clifford, is an entire function of two complex…
- Kelvin functions In applied mathematics, the Kelvin functions berν(x) and beiν(x) are the real and imaginary parts, respectively, of Jν(xe3πi4), where x is real, and Jν(z)…
- Laguerre polynomials In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: xy″+(1−x)y′+ny=…
- Helmholtz equation In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the elliptic partial differential equation:…