A PTA's sky-map resolution is capped at multipoles l~ωL, and the pulsar-term information becomes usable for full-sky mapping only with ~10^11 pulsars, far beyond any realistic array.
A simple derivation of the integrals of products of Legendre polynomials with logarithmic weight
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We explore integrals of products of Legendre polynomials with a logarithmic weight function. More precisely, for Legendre polynomials $P_m$ and $P_n$ of orders $m$ and $n$, respectively, we provide simple derivations of the integrals $$\int \limits_0^1 P_n(2x-1) P_m(2x-1)\log (x)dx.$$
fields
astro-ph.HE 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Gravitational-Wave Sky Mapping with Pulsar Timing Arrays: The Full Earth-Pulsar Response and Fundamental Resolution Limits
A PTA's sky-map resolution is capped at multipoles l~ωL, and the pulsar-term information becomes usable for full-sky mapping only with ~10^11 pulsars, far beyond any realistic array.