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Catalan

Status: Experimental

present and registered, but lightly documented and not yet covered by dedicated tests.

Description

Catalan
    is Catalan's constant, with numerical value ~= 0.915966.
Catalan is the sum over k >= 0 of (-1)^k (2 k + 1)^-2. It is a
mathematical constant: it has attributes Constant and Protected,
NumericQ[Catalan] is True, and D[Catalan, x] is 0. N[Catalan, prec]
evaluates it to any precision.

Examples

No verified examples yet for this function.

Implementation notes

  • Attributes Constant, Protected. `Attributes[Catalan] = {Constant,

Attributes: Constant, Protected.

Implementation status

Experimental — present and registered, but lightly documented and not yet covered by dedicated tests.

References

Notes & additional examples

Worked examples

In[1]:= N[Catalan]
Out[1]= 0.915966

In[1]:= N[Catalan, 40]
Out[1]= 0.91596559417721901505460351493238411077416

In[1]:= D[Catalan, x]
Out[1]= 0

In[1]:= NumericQ[Catalan]
Out[1]= True

In[1]:= N[8 Catalan, 30]
Out[1]= 7.32772475341775212043682811946

Notes

Catalan is Catalan's constant G, the alternating sum over k >= 0 of (-1)^k (2 k + 1)^-2. It is a first-class symbolic constant: it carries the Constant attribute (so D[Catalan, x] is 0), satisfies NumericQ, and N[Catalan, prec] evaluates it to any requested precision via an internal fast-converging series. The 40-digit value matches the standard reference value, and arithmetic combinations such as 8 Catalan are held symbolically until numericalized.