Bessel functions

E554675

mathematical function family special function

Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.

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Observed surface forms (1)

Surface form	Occurrences
Bessel function	1

Statements (49)

Predicate	Object
instanceOf	mathematical function family ⓘ special function ⓘ
appearIn	diffraction and scattering problems ⓘ electromagnetic modes in cylindrical waveguides ⓘ heat conduction in cylindrical rods ⓘ quantum mechanical problems with cylindrical symmetry ⓘ vibration modes of circular membranes ⓘ
ariseAsSolutionsOf	Bessel differential equation ⓘ
ariseInProblemsWith	cylindrical symmetry ⓘ spherical symmetry ⓘ
definedIn	complex plane ⓘ
generalizedBy	hypergeometric functions ⓘ
hasType	Bessel functions of the first kind ⓘ Bessel functions of the second kind ⓘ Hankel functions NERFINISHED ⓘ modified Bessel functions of the first kind ⓘ modified Bessel functions of the second kind ⓘ spherical Bessel functions ⓘ
haveProperty	infinite number of zeros ⓘ integral representations ⓘ orthogonality under suitable weight functions ⓘ recurrence relations ⓘ series expansions ⓘ
haveSubClass	integer-order Bessel functions ⓘ non-integer-order Bessel functions ⓘ
namedAfter	Friedrich Bessel NERFINISHED ⓘ
parameterizedBy	argument ⓘ order ⓘ
relatedTo	Chebyshev polynomials NERFINISHED ⓘ Fourier transform in cylindrical coordinates ⓘ Fourier-Bessel series NERFINISHED ⓘ Gamma function NERFINISHED ⓘ Hankel transform NERFINISHED ⓘ Legendre functions NERFINISHED ⓘ
satisfy	second-order linear ordinary differential equation ⓘ
usedFor	solving Helmholtz equation in cylindrical coordinates ⓘ solving Laplace equation in cylindrical coordinates ⓘ solving diffusion equation in cylindrical coordinates ⓘ
usedIn	acoustics ⓘ antenna theory ⓘ applied mathematics ⓘ electromagnetism ⓘ engineering ⓘ heat conduction theory ⓘ optics ⓘ physics ⓘ random process theory ⓘ signal processing ⓘ wave propagation theory ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Airy disk → describedBy → Bessel functions ⓘ

Friedrich Bessel → notableFor → Bessel functions ⓘ

Friedrich Bessel → hasEponym → Bessel functions ⓘ

this entity surface form: Bessel function

The Fourier Integral and Certain of Its Applications → subject → Bessel functions ⓘ