Harmonic numbers on the HP 50g
06-02-2014, 03:11 PM
Post: #1
 Peter Murphy Junior Member Posts: 44 Joined: Feb 2014
Harmonic numbers on the HP 50g
I recently discovered that the HP 50g function Psi (in MTH NXT SPECIAL) delivers the nth harmonic number:

Hn = Psi(n + 1) – Psi(1)

[and that, by the way, –Psi(1) = 0.577215664902, the Euler constant].

This observation, together with the numerical SOLVE command, allows quick disposal of (say) the problem of finding the smallest integer k for which Hk > 7.6, and it might more generally be useful in mathematics teaching.
06-02-2014, 10:07 PM
Post: #2
 Paul Dale Senior Member Posts: 1,733 Joined: Dec 2013
RE: Harmonic numbers on the HP 50g
I implemented the digamma function for the 34S but it didn't make it in

But where to stop including useful functions....

- Pauli
06-03-2014, 05:41 AM (This post was last modified: 06-03-2014 05:48 AM by Ángel Martin.)
Post: #3
 Ángel Martin Senior Member Posts: 1,261 Joined: Dec 2013
RE: Harmonic numbers on the HP 50g
(06-02-2014 10:07 PM)Paul Dale Wrote:  I implemented the digamma function for the 34S but it didn't make it in
But where to stop including useful functions....

Digamma (Psi) is also useful to obtain the inverse Gamma using Newton's method, there was a thread in the old forum about that but can't find it now.

edit: here's the link

The SandMath has both the harmonic number and Psi functions - the accuracy limited to 10 digits of course.

Cheers,
'AM
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