Gram Series
where
is the Riemann Zeta Function. This approximation to the Prime Counting Function is 10 timesbetter than 
for 
but has been proven to be worse infinitely often by Littlewood (Ingham 1990). An equivalent formulation due toRamanujan 
is
(Berndt 1994), where
is a Bernoulli Number. The integral analog, also found by Ramanujan, is
(Berndt 1994).
References
Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 124-129, 1994. Gram, J. P. ``Underségelser angaaende Maengden af Primtal under en given Graeense.'' K. Videnskab. Selsk. Skr. 2, 183-308, 1884. Ingham, A. E. Ch. 5 in The Distribution of Prime Numbers. New York: Cambridge, 1990. Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, p. 74, 1991.
- Bays' Shuffle
- Beam Detector
- Bean Curve
- Beast Number
- Beatty Sequence
- Beauzamy and Dégot's Identity
- Bee
- Behrens-Fisher Test
- Behrmann Cylindrical Equal-Area Projection
- Bei
- Bell Curve
- Bell Number
- Bellows Conjecture
- Bell Polynomial
- Bell Triangle
- Beltrami Differential Equation
- Beltrami Field
- Beltrami Identity
- Bend (Curvature)
- Bend (Knot)
- Benford's Law
- Benham's Wheel
- Bennequin's Conjecture
- Benson's Formula
- Ber