TCHEBYCHEFF Documentation Error

[John Keith]

The HP 49/50 function TCHEBYCHEFF returns the nth Chebyshev polynomial of the first kind, given an integer n on the stack. The description in the AUR states that n must be a nonnegative integer. In fact, the function actually returns the Chebyshev polynomials of the second kind if given a negative integer argument. The polynomial returned is offset though, so that -n gives U(n-1, X).

Not sure if this is useful to anyone, but it's nice when a bug in the documentation reveals a hidden feature.

[rprosperi]

(12-22-2021 07:41 PM)John Keith Wrote:  Not sure if this is useful to anyone, but it's nice when a bug in the documentation reveals a hidden feature.

Perhaps there's a bug when using negative arguments and that was masked by simply changing the documentation to suggest using only methods that work properly? Not to say that this has ever been done before with product documentation (..cough... <I've done it...> cough).

[KeithB]

I thought you were going to call it out as a spelling error. 8^)

[rprosperi]

(12-23-2021 02:18 PM)KeithB Wrote:  I thought you were going to call it out as a spelling error. 8^)

LOL. Nah, I've seen Chebyshev spelled about every way imaginable, plus a few I would never have imagined.

[Diego Diaz]

Hi there,

Transliterating Russian names is (to say the least) not a simple task. :-)

Although I've seen his (family) name spelled mostly as "Shebyshev", the fact is that the Russian pronunciation is way different from what "Shebyshev" sounds in English.

Some papers, including a letter from the Russian Embassy declares "Tchebycheff" as a French transliteration; being "Shebyshev" its English counterpart.

However, original: [Пафну́тий Льво́вич] Чебышёв, will more likely be pronounced in English as "Tsheebushov". But certainly I'm not proposing yet another variation to include in the current mess. :-D

Just found this post funny and want to share my thoughts... (as wrong as they might be).

Merry Xmas!!

Diego.

[John Keith]

Every modern English-language reference that I have seen uses the spelling "Chebyshev". If "Tchebycheff is the preferred French transliteration, that may explain why the HP 49/50 uses that spelling, since the author of the CAS (our member Bernard Parisse) is, of course, French.

[toml_12953]

(12-24-2021 02:55 AM)Diego Diaz Wrote:  Hi there,

Transliterating Russian names is (to say the least) not a simple task. :-)


Diego.

From Wikipedia:
His name can be alternatively transcribed as Chebysheff, Chebychov, Chebyshov; or Tchebychev, Tchebycheff (French transcriptions); or Tschebyschev, Tschebyschef, Tschebyscheff (German transcriptions); or, rarely, Čebyčev.

Chebychev, a mixture between English and French transliterations, is sometimes[where?] erroneously used.

The correct transliteration according to ISO 9 is Čebyšëv.

The American Mathematical Society adopted the transcription Chebyshev in its Mathematical Reviews.[3]

[telemachos]

Hear Chebyshev pronounced by a couple of native speakers of Russian:

https://forvo.com/word/%D1%87%D0%B5%D0%B...%91%D0%B2/

These polynomials show up (or at least can be made to show up) in the loaded-string problem, and therefore might give rise to interesting activities on (say) the HP-50g:

https://aapt.scitation.org/doi/abs/10.11...alCode=ajp