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=> Algebraic Curves-Mordell Curve
=> Algebraic Curves-Ochoa Curve
=> Algebraic Integer
=> Algebraic Number
=> Algebraic Number Theory
=> Chebotarev Density Theorem
=> Class Field
=> Cyclotomic Field
=> Dedekind Ring
=> Fractional Ideal
=> Global Field
=> Local Field
=> Number Field Signature
=> Picard Group
=> Pisot Number
=> Weyl Sum
=> Casting Out Nines
=> A-Sequence
=> Anomalous Cancellation
=> Archimedes' Axiom
=> B2-Sequence
=> Calcus
=> Calkin-Wilf Tree
=> Egyptian Fraction
=> Egyptian Number
=> Erdős-Straus Conjecture
=> Erdős-Turán Conjecture
=> Eye of Horus Fraction
=> Farey Sequence
=> Ford Circle
=> Irreducible Fraction
=> Mediant
=> Minkowski's Question Mark Function
=> Pandigital Fraction
=> Reverse Polish Notation
=> Division by Zero
=> Infinite Product
=> Karatsuba Multiplication
=> Lattice Method
=> Pippenger Product
=> Reciprocal
=> Russian Multiplication
=> Solidus
=> Steffi Problem
=> Synthetic Division
=> Binary
=> Euler's Totient Rule
=> Goodstein Sequence
=> Hereditary Representation
=> Least Significant Bit
=> Midy's Theorem
=> Moser-de Bruijn Sequence
=> Negabinary
=> Negadecimal
=> Nialpdrome
=> Nonregular Number
=> Normal Number
=> One-Seventh Ellipse
=> Quaternary
=> Radix
=> Regular Number
=> Repeating Decimal
=> Saunders Graphic
=> Ternary
=> Unique Prime
=> Vigesimal
Ziyaretçi defteri
 

Pippenger Product

The Pippenger product is an unexpected Wallis-like formula for e given by

 e/2=(2/1)^(1/2)(2/34/3)^(1/4)(4/56/56/78/7)^(1/8)...
(1)

(Sloane's A084148 and A084149; Pippenger 1980). Here, the nth term for n>=2 is given by

a_n = ([(2^(n-1)-1)!!]^2[(2^n)!!]^2)/(2[(2^(n-1))!!]^2[(2^n-1)!!]^2)
(2)
= (2^(2^n-1)[Gamma(1/2+2^(n-2))]^4)/(pi[Gamma(1/2+2^(n-1))]^2),
(3)

where z!! is a double factorial and Gamma(z) is the gamma function.


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