Title: Confluent Hypergeometric Limit Function -- from Wolfram MathWorld
Open Graph Title: Confluent Hypergeometric Limit Function -- from Wolfram MathWorld
X Title: Confluent Hypergeometric Limit Function -- from Wolfram MathWorld
Description: _0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is implemented in the Wolfram Language as Hypergeometric0F1[b, z]. A Bessel function of the first kind can be expressed in terms of this function by J_n(x)=((1/2x)^n)/(n!)_0F_1(;n+1;-1/4x^2) (4) (Petkovšek et al. 1996).
Open Graph Description: _0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is implemented in the Wolfram Language as Hypergeometric0F1[b, z]. A Bessel function of the first kind can be expressed in terms of this function by J_n(x)=((1/2x)^n)/(n!)_0F_1(;n+1;-1/4x^2) (4) (Petkovšek et al. 1996).
X Description: _0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is implemented in the Wolfram Language as Hypergeometric0F1[b, z]. A Bessel function of the first kind can be expressed in terms of this function by J_n(x)=((1/2x)^n)/(n!)_0F_1(;n+1;-1/4x^2) (4) (Petkovšek et al. 1996).
Opengraph URL: https://mathworld.wolfram.com/ConfluentHypergeometricLimitFunction.html
Domain: mathworld.wolfram.com
| DC.Title | Confluent Hypergeometric Limit Function |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | _0F_1(;a;z)=lim_(q->infty)_1F_1(q;a;z/q). (1) It has a series expansion _0F_1(;a;z)=sum_(n=0)^infty(z^n)/((a)_nn!) (2) and satisfies z(d^2y)/(dz^2)+a(dy)/(dz)-y=0. (3) It is implemented in the Wolfram Language as Hypergeometric0F1[b, z]. A Bessel function of the first kind can be expressed in terms of this function by J_n(x)=((1/2x)^n)/(n!)_0F_1(;n+1;-1/4x^2) (4) (Petkovšek et al. 1996). |
| DC.Subject | 33C20 |
| 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/ConfluentHypergeometricLimitFunction.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_ConfluentHypergeometricLimitFunction.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_ConfluentHypergeometricLimitFunction.png |
| None | ie=edge |
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