Inverse Harmonic and Inverse Digamma Functions (HP 49G (*) and HP 50g )

[Gerson W. Barbosa]

(04-27-2016 04:57 PM)John Keith Wrote:  Cool, thanks! I was just trying to figure out an inverse harmonic number function the other day and getting nowhere. Neither Mathworld nor Wikipedia seemed to have much to say on the subject.

Thanks for your interest!

If the arguments are always plain harmonic numbers, that is, the ones obtained from the discrete function, then the inverse function can be implemented simply as

InvHn:

« .577215664902 - EXP IP »

Examples:

137 ENTER 60 / InvHn --> 5. ; 137/60 = H(5)

10 Hx --> 2.92896825397 ; H(10)
InvHn --> 10.

2E10 --> 24.2962137754 ; H(2x10^10)
InvHn --> 20000000000.

where Hx is the program for the continuous function:

Hx:

« 1. + Psi .577215664902 + »

Regards,

Gerson.