https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13001 Wed 11 Apr 2018 14:09:36 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14235 h(s,t) can be evaluated in terms of Riemann ζ-functions when s + t is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we give a formula for the series [unable to replicate formula]. This evaluation involves ζ-functions and σ_h(2,m).]]> Wed 11 Apr 2018 10:48:46 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14081 b-1 =1 are given parameters, f R → R is the unknown. We show that there is a unique bounded function f which solves (F) and satisfies f(t) = 0 for t <~-1/(1 − a), f(t) = 1 for t > 1/(1 − a). This solution can be interpreted as the distribution function of a certain random series. It is known to be either singular or absolutely continuous, but the problem for which parameters it is absolutely continuous is largely open. We collect some previously established partial answers and generalize them. We also point out an interesting connection to the so-called Schilling equation.]]> Tue 06 May 2014 12:35:55 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14064 Sat 24 Mar 2018 08:22:33 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14690 i with Σx_i ≥0 , the estimate Σx_i e^xi ≥ C_N/N Σ x²/_i holds, where C_N = max{2, e (1 − 1/N)} . We also prove analogues for the 1-norm and for Lebesgue-integrable functions.]]> Sat 24 Mar 2018 08:19:10 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13127 Sat 24 Mar 2018 08:15:42 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13080 Sat 24 Mar 2018 08:15:38 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:10337 Sat 24 Mar 2018 08:06:59 AEDT ]]>