https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Hankel determinants of zeta values https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:25545 Wed 11 Apr 2018 17:10:43 AEST ]]> Well-poised hypergeometric service for diophantine problems of zeta values https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11942 Wed 11 Apr 2018 17:04:41 AEST ]]> On the irrationality of generalized q-logarithm https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:26657 1, and generic rational x and z, we establish the irrationality of the series [formula could not be replicated].It is a symmetric (ℓ_p(x,z)=ℓ_p(z,x)) generalization of the q-logarithmic function (x = 1 and p = 1/q where |q|<1), which in turn generalizes the q-harmonic series (x = z = 1). Our proof makes use of the Hankel determinants built on the Padé approximations to ℓ_p(x,z).]]> Wed 11 Apr 2018 15:04:15 AEST ]]> Irrationality of certain numbers that contain values of the di- and trilogarithm https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10010 Wed 11 Apr 2018 12:43:40 AEST ]]> New irrationality measures for q-logarithms https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11927 q(1-z) = [formula could not be replicated], |z| ≤ 1, when p = 1/q ∈ℤ{0,±1} and z∈ℚ.]]> Wed 11 Apr 2018 10:51:29 AEST ]]> An elementary proof of the irrationality of Tschakaloff series https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11923 q(z)= ∞/∑/n=0 zⁿq^-n(n-1)/2 in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to T_q(z).]]> Sat 24 Mar 2018 11:09:02 AEDT ]]> On the non-quadraticity of values of the q-exponential function and related q-series https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11917 q(z;λ)=[formula could not be replicated], |q|>1, λ ∉ q^ℤ>0 that includes as special cases the Tschakaloff function (λ = 0) and the q-exponential function (λ = 1). In particular, we prove the non-quadraticity of the numbers F_{q/sub>(α;λ) for integral q, rational λ and α ∉ -λq^ℤ>0, α ≠ 0.]]>} Sat 24 Mar 2018 11:09:01 AEDT ]]> Euler’s constant, q-logarithms, and formulas of Ramanujan and Gosper https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10331 Sat 24 Mar 2018 11:07:38 AEDT ]]> Heine's basic transform and a permutation group for q-harmonic series https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11940 Sat 24 Mar 2018 10:31:59 AEDT ]]> Rational approximations to a q-analogue of π and some other q-series. https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:15720 Sat 24 Mar 2018 08:25:20 AEDT ]]> On simultaneous diophantine approximations to ζ(2) and ζ(3) https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:19583 Sat 24 Mar 2018 07:58:20 AEDT ]]> A determinantal approach to irrationality https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32649 n/q_n with integral p_n and q_n such that q_nξ−p_n≠0 for all n and q_nξ−p_n→0 as n→∞. In this paper, we give an extension of this criterion in the case when the sequence possesses an additional structure; in particular, the requirement q_nξ−p_n→0 is weakened. Some applications are given, including a new proof of the irrationality of π. Finally, we discuss analytical obstructions to extend the new irrationality criterion further and speculate about some mathematical constants whose irrationality is still to be established.]]> Mon 23 Sep 2019 10:53:04 AEST ]]>