https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12926 4(± 1) are given and two new conjectures are recorded.]]> Wed 11 Apr 2018 13:49:54 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12331 Wed 11 Apr 2018 10:18:35 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12973 Wed 11 Apr 2018 09:50:53 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12247 Wed 11 Apr 2018 09:16:08 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11902 n(x). His result was a consequence of Bailey’s identity for a special case of Appell’s hypergeometric function of the fourth type. In this paper, we present a generalisation of Bailey’s identity and its implication to generating functions of Legendre polynomials of the form Σ^∞/_n=0 u_nP_n(x)zⁿ, where u_n is an Apéry-like sequence, that is, a sequence satisfying (n + 1)²u_n+1 = (an² + an + b)u_n − cn²u_n−1, where n ≥ 0 and u₋₁ = 0, u₀ = 1. Using both Brafman’s generating functions and our results, we also give generating functions for rarefied Legendre polynomials and construct a new family of identities for 1/π.]]> Thu 29 Mar 2018 14:30:13 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:18575 Sun 28 Jun 2015 17:38:19 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11904 Sat 24 Mar 2018 08:08:57 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:16327 Sat 24 Mar 2018 07:58:01 AEDT ]]>