Mathematical constants who can be represented by BBP-type formula have the property that their n-th digit can be directly calculated without needing to compute any of the first (n-1) digits. This online database presents a comprehensive compilation of both formal and experimental BBP-type formulae.

Constants and expressions can be entered using correct Maple syntax. For example: Pi, arctan(2), Zeta(2), Catalan.

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BBP-type Formula Database

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Constant (by name) Formula Reference Constant (enter text) : All constants 0 Pi Pi^2 Pi^3 Pi^4 ln(3) ln(5) ln(7) ln(2) ln(11) ln(13) ln(3)^2 Zeta(5) ln(Phi) ln(2)^5 ln(2)^4 ln(2)^3 Zeta(3) Catalan ln(3/2) ln(2)^2 ln(9/10) Pi*ln(2) arctan(2) Pi^4*ln(2) Pi*2^(1/2) Pi*3^(1/2) Pi*ln(2)^2 Pi^2*ln(2) arctan(4/5) Pi^2*ln(2)^3 Pi^2*ln(2)^2 5^(1/2)*ln(Phi) Pi*3^(1/2)*ln(2) Pi*3^(1/2)*ln(3) 3^(1/2)*Cl_2(Pi/3) Catalan-1/8*Pi*ln(2) 2^(1/2)*ln(1+2^(1/2)) 35*Zeta(3)-2*Pi^2*ln(2) ln(1111111111/387420489) 3^(1/2)*arctan(1/7*3^(1/2)) 2^(1/2)*arctan(1/2*2^(1/2)) 13*Zeta(3)-Pi^2*ln(3)+ln(3)^3 13/3*Zeta(3)+1/8*ln(3)^3-5/24*Pi^2*ln(3) 1/3*ln(2)^3-5/12*Pi^2*ln(2)+35/4*Zeta(3) 1/3*3^(1/2)*(29/1296*Pi^3-1/48*Pi*ln(3)^2) 127/5184*Pi^4-1/32*Pi^2*ln(3)^2+5/192*ln(3)^4 20*Cl_4(Pi/2)+3*Pi*ln(2)^3/32-27*Pi^3*ln(2)/128 12*Cl_4(Pi/2)+29*Pi*ln(2)^3/192-47*Pi^3*ln(2)/256 1/3^(1/2)(11*Cl_4(Pi/3)-29*Pi^3*ln(3)/288+Pi*ln(3)^3/32) 1573*Zeta(3)-1/128*ln(3)^5+1/64*Pi^2*ln(3)^3-127/3456*Pi^4*ln(3) / P( , , , A)

Found a new BBP-type formula? Add your formula to the database.

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(c) 2011 Written by Matthew Tam with assistance from David Allingham, David Bailey, Jon Borwein and Andrew Mattingly.