Catalan

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

General characteristics

The Catalan's number C is a constant. It is a positive real number. Whether C is irrational is not known.

Series representations

Generalized power series

G.Huvent (2006)

Integral representations

On the real axis

Of the direct function

Involving the direct function

Multiple integral representations

Continued fraction representations

Complex characteristics

Real part

Imaginary part

Absolute value

Argument

Conjugate value

Signum value

Differentiation

Low-order differentiation

Fractional integro-differentiation

Integration

Indefinite integration

Integral transforms

Fourier exp transforms

Inverse Fourier exp transforms

Fourier cos transforms

Fourier sin transforms

Laplace transforms

Inverse Laplace transforms

Representations through more general functions

Through hypergeometric functions

Involving HypergeometricPFQ

Through Meijer G

Classical cases

Through other functions

Inequalities

History

– E. Catalan (1865, 1883)
– M. Leclert (1865)
– M. Bresse (1867)
– J. W. L. Glaisher (1877)

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