Add to ORKGWe demonstrate that also the second sum involved in Apéry’s proof of the irrationality of ζ(3) becomes trivial by symbolic summation. In his beautiful survey [4], van der Poorten explained that Apéry’s proof [1] of the irrationality of ζ(3) relies on the following fact: If and b(n) = k=0 a(n) = n� � �2 � �2 n + k n k k k=0 n� � �2 � � �
AbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumC...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
AbstractUsing Padé approximants to the asymptotic expansion of the error term for the series ∑k=1∞ 1...
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
Let a; b; c be positive integers and define the so-called triple, double and single Euler sums by ζ(...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
We present a new, rather elementary, proof of the irrationality of ζ(3) based on some recent ‘hyperg...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
A right of passage to theoretical mathematics is often a proof of the irrationality of√ 2, or at lea...
Abstract. Freek Wiedijk proposed the well-known theorem about the irrationality of 2 as a case study...
We present a hypergeometric construction of rational approximations to ζ(2) and ζ(3) which allows on...
Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven’s proof to show that e...
International audienceThis paper presents a complete formal verification of a proof that the evaluat...
AbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumC...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...
AbstractUsing Padé approximants to the asymptotic expansion of the error term for the series ∑k=1∞ 1...
In 1978, Apéry [2] proved the irrationality of ζ(3) by constructing two explicit sequences of integ...
Let a; b; c be positive integers and define the so-called triple, double and single Euler sums by ζ(...
Denote by sigma(k)(n) the sum of the k-th powers of the divisors of n, and let S-k = Sigma(n >= 1) (...
We present a new, rather elementary, proof of the irrationality of ζ(3) based on some recent ‘hyperg...
AbstractApéry introduced a recurrence relation for a proof of the irrationality of ζ(3). Let an (n ≥...
For positive integers $k$ and $n$ let $\sigma_k(n)$ denote the sum of the $k$th powers of the diviso...
A right of passage to theoretical mathematics is often a proof of the irrationality of√ 2, or at lea...
Abstract. Freek Wiedijk proposed the well-known theorem about the irrationality of 2 as a case study...
We present a hypergeometric construction of rational approximations to ζ(2) and ζ(3) which allows on...
Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven’s proof to show that e...
International audienceThis paper presents a complete formal verification of a proof that the evaluat...
AbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumC...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn + k) and un = Σ0n(kn)2(kn + k)2 in ...
AbstractIn 1979 R. Apéry introduced the numbers an = Σ0n(kn)2(kn+k)2 in his irrationality proof for ...