### Abstract

This entry provides Landau symbols to describe and reason about the asymptotic growth of functions for sufficiently large inputs. A number of simplification procedures are provided for additional convenience: cancelling of dominated terms in sums under a Landau symbol, cancelling of common factors in products, and a decision procedure for Landau expressions containing products of powers of functions like x, ln(x), ln(ln(x)) etc.

### License

BSD License

### Topics

- Mathematics/Analysis

### Session Landau_Symbols

- Group_Sort
- Landau_Real_Products
- Landau_Simprocs
- Landau_More

### Used by

- The Error Function
- Dirichlet L-Functions and Dirichlet’s Theorem
- Dirichlet Series
- CryptHOL
- Expected Shape of Random Binary Search Trees
- Lower bound on comparison-based sorting algorithms
- The number of comparisons in QuickSort
- The Euler–MacLaurin Formula
- Stirling’s formula
- Catalan Numbers
- The Akra-Bazzi theorem and the Master theorem

## Cite

×

Landau_Symbols-AFP

    @article{Landau_Symbols-AFP,
      author  = {Manuel Eberl},
      title   = {Landau Symbols},
      journal = {Archive of Formal Proofs},
      month   = {July},
      year    = {2015},
      note    = {\url{https://isa-afp.org/entries/Landau_Symbols.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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