Riemann Function
The function obtained by approximating the Riemann Weighted Prime-Power Counting Function 
in
 | (1) |
. This gives |  |  | (2) |
 |  | (3) |
where
is the Riemann Zeta Function, 
is the Möbius Function, and is the Logarithmic Integral. Then | (4) |
is the Prime Counting Function. Ramanujan independently derived the formula for 
, but nonrigorously (Berndt 1994, p. 123).See also Mangoldt Function, Prime Number Theorem, Riemann-Mangoldt Function, Riemann Zeta Function
References
Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, 1994. Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 144-145, 1996. Riesel, H. and Göhl, G. ``Some Calculations Related to Riemann's Prime Number Formula.'' Math. Comput. 24, 969-983, 1970. Wagon, S. Mathematica in Action. New York: W. H. Freeman, pp. 28-29 and 362-372, 1991.
- Legendre Polynomial
- Legendre Polynomial of the Second Kind
- Legendre Quadrature
- Legendre Relation
- Legendre's Chi-Function
- Legendre's Constant
- Legendre Series
- Legendre's Factorization Method
- Legendre's Formula
- Legendre's Quadratic Reciprocity Law
- Legendre Sum
- Legendre Symbol
- Legendre Transformation
- Lehmer Method
- Lehmer Number
- Lehmer-Schur Method
- Lehmer's Constant
- Lehmer's Formula
- Lehmer's Phenomenon
- Lehmer's Problem
- Lehmer's Theorem
- Lehmus' Theorem
- Leibniz Criterion
- Leibniz Harmonic Triangle
- Leibniz Identity