The modified spherical Bessel differential equation is given by the spherical Bessel differential equation with a negative separation constant,
![r^2(d^2R)/(dr^2)+2r(dR)/(dr)-[r^2+n(n+1)]R=0.](/images/equations/ModifiedSphericalBesselDifferentialEquation/NumberedEquation1.svg) |
The solutions are called modified spherical Bessel functions of the first and second kinds.
Modified Spherical Bessel Differential Equation
See also
Modified Spherical Bessel Function of the First Kind, Modified Spherical Bessel Function of the Second Kind, Spherical Bessel Differential EquationExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). §10.2.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 374-377, 1972.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 121, 1997.Referenced on Wolfram|Alpha
Modified Spherical Bessel Differential EquationCite this as:
Weisstein, Eric W. "Modified Spherical Bessel Differential Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ModifiedSphericalBesselDifferentialEquation.html