CatalanNumber[-1] formula on functions.wolfram.com unequals result from Mathematica

Question

The formula for CatalanNumber[-1] on this functions.wolfram.com page gives:

-(1/2)

whereas CatalanNumber[-1] directly evaluated gives?

-1

Mathematica isn't consistent with itself. (CatalanNumber[n] // FunctionExpand) /. n -> -1 evaluates to -1/2. You should report this to Wolfram Support — Bob Hanlon, Nov 02 '17 at 21:08
This exact input mentioned in the Possible Issues section here: http://reference.wolfram.com/language/ref/CatalanNumber.html — Greg Hurst, Nov 03 '17 at 02:05

J. M.'s missing motivation · Accepted Answer · 2017-11-03T02:51:19.957

9

This is ~~a bug~~ an enforced convention in CatalanNumber[] (per Chip). Evaluating

Needs["GeneralUtilities`"]
PrintDefinitions[CatalanNumber]

reveals that the definition CatalanNumber[-1] := -1 was hard-coded.

Thus, do this for now if you want the gamma function representation's limiting value:

FunctionExpand[CatalanNumber[n]] /. n -> -1
   -1/2

edited Nov 03 '17 at 02:51

answered Nov 02 '17 at 21:08

1 Answers1