# Newton series expansion of bosonic operator functions

### Submission summary

 As Contributors: Fred Hucht Arxiv Link: https://arxiv.org/abs/2008.11139v1 (pdf) Date submitted: 2020-08-26 11:56 Submitted by: Hucht, Fred Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approach: Theoretical

### Abstract

We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms. As a second example, we show that factorial moments and factorial cumulants arising in the context of photon or electron counting are a natural consequence of Newton series expansions.

###### Current status:
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