inverse linear

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21: 2.9 Difference Equations

… ►Many special functions that depend on parameters satisfy a three-term linear recurrence relation …or equivalently the second-order homogeneous linear difference equation … ►This situation is analogous to second-order homogeneous linear differential equations with an irregular singularity of rank 1 at infinity (§2.7(ii)). … ►For asymptotic expansions in inverse factorial series see Olde Daalhuis (2004a). … ►For an introduction to, and references for, the general asymptotic theory of linear difference equations of arbitrary order, see Wimp (1984, Appendix B). …

22: 1.13 Differential Equations

… ►For extensions of these results to linear homogeneous differential equations of arbitrary order see Spigler (1984). … ►As the interval

[a,b]

is mapped, one-to-one, onto

[0,c]

by the above definition of

t

, the integrand being positive, the inverse of this same transformation allows

\widehat{q}(t)

to be calculated from

p,q,\rho

in (1.13.31),

p,\rho\in C^{2}(a,b)

and

q\in C(a,b)

. …