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Lah number
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== Practical application == In recent years, Lah numbers have been used in [[steganography]] for hiding data in images. Compared to alternatives such as [[Discrete cosine transform|DCT]], [[Discrete Fourier transform|DFT]] and [[Discrete wavelet transform|DWT]], it has lower complexity of calculation—<math>O(n \log n)</math>—of their integer coefficients.<ref>{{Cite journal |last1=Ghosal |first1=Sudipta Kr |last2=Mukhopadhyay |first2=Souradeep |last3=Hossain |first3=Sabbir |last4=Sarkar |first4=Ram |year=2020 |title=Application of Lah Transform for Security and Privacy of Data through Information Hiding in Telecommunication |journal=Transactions on Emerging Telecommunications Technologies |volume=32 |issue=2 |doi=10.1002/ett.3984|s2cid=225866797 }}</ref><ref>{{Cite web |title=Image Steganography-using-Lah-Transform |url=https://in.mathworks.com/matlabcentral/fileexchange/78751-image-steganography-using-lah-transform |website=MathWorks|date=5 June 2020 }}</ref> The Lah and Laguerre transforms naturally arise in the perturbative description of the [[chromatic dispersion]].<ref>{{Cite journal|last1=Popmintchev|first1=Dimitar|last2=Wang|first2=Siyang|last3=Xiaoshi |first3=Zhang |last4=Stoev|first4=Ventzislav|last5=Popmintchev|first5=Tenio|date=2022-10-24 |title=Analytical Lah-Laguerre optical formalism for perturbative chromatic dispersion|journal=[[Optics Express]]|volume=30|issue=22|pages=40779β40808|doi=10.1364/OE.457139|doi-access=free|pmid=36299007 |bibcode=2022OExpr..3040779P}}</ref><ref>{{cite arXiv|last1=Popmintchev|first1=Dimitar|last2=Wang|first2=Siyang|last3=Xiaoshi|first3=Zhang |last4=Stoev|first4=Ventzislav|last5=Popmintchev|first5=Tenio|date=2020-08-30|title= Theory of the Chromatic Dispersion, Revisited |class=physics.optics |eprint=2011.00066}}</ref> In [[Lah-Laguerre optics]], such an approach tremendously speeds up optimization problems.
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