https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:25545 Wed 11 Apr 2018 17:10:43 AEST ]]> https://nova.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 ]]> https://nova.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 ]]> https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:31577 Sat 24 Mar 2018 08:45:03 AEDT ]]> https://nova.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 ]]>