confluent hypergeometric function

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:software
gptkbp:alsoKnownAs	gptkb:Kummer's_function
gptkbp:application	gptkb:probability_theory mathematical physics quantum mechanics statistics
gptkbp:category	gptkb:mathematical_concept
gptkbp:definedIn	partial differential equations
gptkbp:differential	z d^2w/dz^2 + (b-z) dw/dz - a w = 0
gptkbp:domain	complex numbers
gptkbp:generalizes	gptkb:hypergeometric_function
gptkbp:hasSpecialCase	gptkb:Laguerre_polynomials gptkb:Hermite_polynomials gptkb:generalized_hypergeometric_function Bessel function exponential function
https://www.w3.org/2000/01/rdf-schema#label	confluent hypergeometric function
gptkbp:introduced	gptkb:Ernst_Kummer
gptkbp:notation	M(a, b, z) _1F_1(a; b; z)
gptkbp:parameter	a b z
gptkbp:relatedTo	gptkb:Whittaker_function gptkb:Gauss_hypergeometric_function gptkb:Tricomi's_function
gptkbp:seriesExpansion	sum_{n=0}^∞ (a)_n z^n / [(b)_n n!]
gptkbp:usedIn	solutions to Schrödinger equation solutions to differential equations
gptkbp:bfsParent	gptkb:Kummer's_function gptkb:parabolic_cylinder_function
gptkbp:bfsLayer	6