Inverse spherical Bessel functions generalize Lambert W and solve similar equations containing trigonometric or hyperbolic subexpressions or their inverses

A strict integer Laurent polynomial in a variable x is 0 or a sum of one or more terms having integer coefficients times x raised to a negative integer exponent. Equations that can be transformed to certain such polynomials times exp(-x) = constant are exactly solvable by inverses of modified spherical Bessel functions of the second kind kₙ(x) where n is the order, generalizing the Lambert W function when n > 0. Equations that can be converted to certain such polynomials times cos(x) or such polynomials times sin(x) or a sum thereof = constant are exactly solvable by inverses of spherical Bessel functions yₙ(x) or jₙ(x). Such equations include cos(x)/x = constant, for which the solution inverse₁(y₀)(-constant) is the Dottie number when constant = 1, where subscript 1 is the branch number. Equations that can be converted to certain strict integer Laurent polynomials times sinh(x) and possibly also plus such a polynomial times cosh(x) are exactly solvable by inverses of modified spherical Bessel functions of the first kind iₙ(x). Abstract These discoveries arose from the AskConstants program surprisingly proposing the explicit exact closed form solution inverse₁(y₀)(-1) for the approximate input 0.739085133215160642, because no explicit exact closed form representation was known for this Dottie number from approximately 1865 to 2022. This article includes descriptions of how to implement such multi-branched real inverses.