Reciprocal series

Definitions

  • Chambers's Twentieth Century Dictionary
    • Reciprocal series a series each of whose terms is the reciprocal of the corresponding term of another series
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Etymology

Chambers's Twentieth Century Dictionary
L.,—serĕre, sertum, to join.

Usage


In science:

In particular, for each fixed λ 6= 0, lim supn→∞ (mn (λ))1/n is the reciprocal of the radius of convergence of the series expansion of eG(z , λ) at z = 0.
Large deviations for the leaves in some random trees
Variations on computing reciprocals of power series.
A simple and fast algorithm for computing exponentials of power series
E (~r , ω ), where the crystal’s spatially periodic dielectric permittivity can be represented as the Fourier series: ε(~r, ω ) = P ετ (ω )ei~τ r , ~τ is the reciprocal lattice vector.
Spontaneous and Induced Radiation by Relativistic Particles in Natural and Photonic Crystals. Crystal X-ray Lasers and Volume Free Electron Lasers (VFEL)
We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian.
Reciprocity and rationality for the greedy normal form of a Coxeter group
As corollaries we obtain many of the known rationality and reciprocity results for the growth series of Coxeter groups as well as some new ones.
Reciprocity and rationality for the greedy normal form of a Coxeter group
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