92 citations · 266 across the 43 of their papers we have counts for
49 papers
Irrationality and Transcendence of Alternating Series Via Continued Fractions
Jonathan Sondow
Euler gave recipes for converting alternating series of two types, I and II, into equivalent continued fractions, i.e., ones whose convergents equal the partial sums. A condition w…
On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base- digits
Bernd C. Kellner, Jonathan Sondow
We give a new characterization of the set of Carmichael numbers in the context of -adic theory, independently of the classical results of Korselt and Carmichael. T…
Extending Babbage's (Non-)Primality Tests
Jonathan Sondow
We recall Charles Babbage's 1819 criterion for primality, based on simultaneous congruences for binomial coefficients, and extend it to a least-prime-factor test. We also prove a p…
Primary Pseudoperfect Numbers, Arithmetic Progressions, and the Erdős-Moser Equation
Jonathan Sondow, Kieren MacMillan
A primary pseudoperfect number (PPN) is an integer such that the reciprocals of and its prime factors sum to 1. PPNs arise in studying perfectly weighted graphs and sin…
On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
John M. Campbell, Jacopo D'Aurizio, Jonathan Sondow
Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integra…
Power-Sum Denominators
Bernd C. Kellner, Jonathan Sondow
The power sum has been of interest to mathematicians since classical times. Johann Faulhaber, Jacob Bernoulli, and others who followed expressed power su…