Title: Spherical Bessel Function of the First Kind -- from Wolfram MathWorld
Open Graph Title: Spherical Bessel Function of the First Kind -- from Wolfram MathWorld
X Title: Spherical Bessel Function of the First Kind -- from Wolfram MathWorld
Description: The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind and, in general, z and nu are complex numbers. The function is most commonly encountered in the case nu=n an integer, in which case it is given by j_n(z) = 2^nz^nsum_(k=0)^(infty)((-1)^k(k+n)!)/(k!(2k+2n+1)!)z^(2k) (2) = z^nsum_(k=0)^(infty)((-1)^k)/(k!(2k+2n+1)!!)((z^2)/2)^k (3) = (-1)^nz^n(d/(zdz))^n(sinz)/z....
Open Graph Description: The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind and, in general, z and nu are complex numbers. The function is most commonly encountered in the case nu=n an integer, in which case it is given by j_n(z) = 2^nz^nsum_(k=0)^(infty)((-1)^k(k+n)!)/(k!(2k+2n+1)!)z^(2k) (2) = z^nsum_(k=0)^(infty)((-1)^k)/(k!(2k+2n+1)!!)((z^2)/2)^k (3) = (-1)^nz^n(d/(zdz))^n(sinz)/z....
X Description: The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind and, in general, z and nu are complex numbers. The function is most commonly encountered in the case nu=n an integer, in which case it is given by j_n(z) = 2^nz^nsum_(k=0)^(infty)((-1)^k(k+n)!)/(k!(2k+2n+1)!)z^(2k) (2) = z^nsum_(k=0)^(infty)((-1)^k)/(k!(2k+2n+1)!!)((z^2)/2)^k (3) = (-1)^nz^n(d/(zdz))^n(sinz)/z....
Opengraph URL: https://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html
Domain: mathworld.wolfram.com
| DC.Title | Spherical Bessel Function of the First Kind |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind and, in general, z and nu are complex numbers. The function is most commonly encountered in the case nu=n an integer, in which case it is given by j_n(z) = 2^nz^nsum_(k=0)^(infty)((-1)^k(k+n)!)/(k!(2k+2n+1)!)z^(2k) (2) = z^nsum_(k=0)^(infty)((-1)^k)/(k!(2k+2n+1)!!)((z^2)/2)^k (3) = (-1)^nz^n(d/(zdz))^n(sinz)/z.... |
| DC.Date.Modified | 2007-03-14 |
| DC.Subject | 33C10 |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/SphericalBesselFunctionoftheFirstKind.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2007-03-14 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_SphericalBesselFunctionoftheFirstKind.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_SphericalBesselFunctionoftheFirstKind.png |
| None | ie=edge |
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