Confluent hypergeometric function information

mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential...

ordinary hypergeometric function 2F1(a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as...

(Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special...

mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by...

{z^{s+k}}{s+k}}={\frac {z^{s}}{s}}M(s,s+1,-z),} where M is Kummer's confluent hypergeometric function. When the real part of z is positive, γ ( s , z ) = s − 1...

Confluent hypergeometric functions of the first kind. The conventional Hermite polynomials may also be expressed in terms of confluent hypergeometric...

characteristic function of the beta distribution to a Bessel function, since in the special case α + β = 2α the confluent hypergeometric function (of the first...

; z ) {\displaystyle \;_{1}F_{1}(a;b;z)=M(a;b;z)} is the confluent hypergeometric function. Other pairs of independent solutions may be formed from linear...

function Riesz function Hypergeometric functions: Versatile family of power series. Confluent hypergeometric function Associated Legendre functions Meijer G-function...

real-valued, Γ(x) is the gamma function and 1F1(a, b; x) is a confluent hypergeometric function. Some subfamilies of hypergeometric-Gaussian (HyGG) modes can...

{i^{l}}{(m+nl+1)}}{\frac {x^{m+nl+1}}{l!}}} is a confluent hypergeometric function and also an incomplete gamma function ∫ x m e i x n d x = x m + 1 m + 1 1 F 1...

Coulomb potential and can be written in terms of confluent hypergeometric functions or Whittaker functions of imaginary argument. The Coulomb wave equation...

Mittag-Leffler function, and can also be expressed as a confluent hypergeometric function (Kummer's function): erf ⁡ x = 2 x π M ( 1 2 , 3 2 , − x 2 ) . {\displaystyle...

stationary one-dimensional Schrödinger equation in terms of the confluent hypergeometric functions. The potential is given as V = V 0 1 + W ( e − x σ ) . {\displaystyle...

{1}{(1-t)^{\alpha +1}}}e^{-tx/(1-t)}.} Laguerre functions are defined by confluent hypergeometric functions and Kummer's transformation as L n ( α ) ( x...

, z ) {\displaystyle M(a,b,z)} is Kummer's confluent hypergeometric function. The characteristic function is given by: φ ( t ; k ) = M ( k 2 , 1 2 , −...

In mathematics, the Bateman function (or k-function) is a special case of the confluent hypergeometric function studied by Harry Bateman(1931). Bateman...

where 1F1 is the confluent hypergeometric function and J1 is the Bessel function of the first kind. Likewise the moment generating function can be calculated...

a=0.} Another connexion with the confluent hypergeometric functions is that E1 is an exponential times the function U(1,1,z): E 1 ( z ) = e − z U ( 1...

the plain and absolute moments can be expressed in terms of confluent hypergeometric functions 1 F 1 {\displaystyle {}_{1}F_{1}} and U . {\displaystyle U...

confluent hypergeometric series 1F1 of one variable and the confluent hypergeometric limit function 0F1 of one variable. The first of these double series was...

b ; z ) {\displaystyle M(a,b,z)=_{1}F_{1}(a;b;z)} is the confluent hypergeometric function of the first kind. When k is even, the raw moments become...

deviation of 1. R has a known density that can be expressed as a confluent hypergeometric function. The distribution of the reciprocal of a t distributed random...

the 24 symmetries of the hypergeometric differential equations obtained by Kummer. The symmetries fixing the local Heun function form a group of order 24...