RamanujanTau

Notations

Traditional name

Traditional notation

Mathematica StandardForm notation

Primary definition

Specific values

Values at fixed points

General characteristics

Domain and analyticity

τ(n) is a nonanalytical function which is defined for nonnegative integer n.

Symmetries and periodicities

Symmetry

No symmetry

Periodicity

No periodicity

Series representations

Asymptotic series expansions

Transformations

Multiple arguments

Identities

Functional identities

Summation

Infinite summation

Representations through equivalent functions

With related functions

Involving other related functions

Inequalities

History

– S. Ramanujan (1916)
– L.J. Mordell (1917) proved that τ(n) is a multiplicative function
– Hardy (1927)
– Wilton (1929)
– G.N. Watson (1935)
– Walfisz (1938)
– Bambah and Chowla (1947)
– Sengupta (1948)
– van der Blij (1948)

Copyright