The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table.

1. tau(n) is an alternate notation for the divisor function d(n)=sigma_0(n).

2. tau=omega_1/omega_2 is the half-period ratio of an elliptic function.

3. tau(n) denotes the tau function of Ramanujan, defined by the generating function


4. tau is used as an alternate notation for the golden ratio phi.

5. As a characteristic time for exponential decay or growth, i.e., e^(-t/tau).

The symbol also has a number of other different meanings in physics, for example the tau particle, tau neutrino, as a symbol for torque, etc.

See also

Divisor Function, Half-Period Ratio, Tau Conjecture, Tau Dirichlet Series, Tau Function

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Cite this as:

Weisstein, Eric W. "Tau." From MathWorld--A Wolfram Web Resource.

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