On the monotonicity of the correction term in Ramanujan's factorial approximation

Mark B. Villarino; Daniel Campos Salas; Javier Carvajal Rojas

doi:10.1017/S002555720000591X

On the monotonicity of the correction term in Ramanujan's factorial approximation

Classical Analysis and ODEs 2022-03-01 v1

Authors: Mark B. Villarino , Daniel Campos Salas , Javier Carvajal Rojas

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Abstract

We present two new proofs of the monotonicity of the correction term $\theta_n$ in Ramanujan's refinement of Stirling's formula.

Keywords

Ramanujan's factorial approximation Stirling's formula correction term monotonicity mathematical proof

Cite

@article{arxiv.1112.1896,
  title  = {On the monotonicity of the correction term in Ramanujan's factorial approximation},
  author = {Mark B. Villarino and Daniel Campos Salas and Javier Carvajal Rojas},
  journal= {arXiv preprint arXiv:1112.1896},
  year   = {2022}
}