Hyperbolic functions: Difference between revisions

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m Useful relations: ce ("Euclidean" in upper case in book title)
Hyperbolic tangent{{anchor|tanh}}: spelling correction and conversion to first/lastname par.s in one ref.
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===Hyperbolic tangent{{anchor|tanh}}===
 
The hyperbolic tangent is the (unique) solution to the [[differential equation]] {{math|1=''f''&thinsp;′ = 1 − ''f''&thinsp;<sup>2</sup>}}, with {{math|1=''f''&hairsp;(0) = 0}}.<ref>{{cite book |title=Nonlinear Workbook, The: Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic With C++, Java And Symbolicc++ Programs |author1first=Willi-hansHans |last= Steeb |edition= 3rd|publisher=World Scientific Publishing Company |year=2005 |isbn=978-981-310-648-2 |page=281 |url=https://books.google.com/books?id=-Qo8DQAAQBAJ}} [https://books.google.com/books?id=-Qo8DQAAQBAJ&pg=PA281 Extract of page 281 (using lambda=1)]</ref><ref>{{cite book |title=An Atlas of Functions: with Equator, the Atlas Function Calculator |author1=Keith B. Oldham |author2=Jan Myland |author3=Jerome Spanier |edition=2nd, illustrated |publisher=Springer Science & Business Media |year=2010 |isbn=978-0-387-48807-3 |page=290 |url=https://books.google.com/books?id=UrSnNeJW10YC}} [https://books.google.com/books?id=UrSnNeJW10YC&pg=PA290 Extract of page 290]</ref>
 
==Useful relations==