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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Transformations > Some functions of arguments





http://functions.wolfram.com/01.06.16.0165.01









  


  










Input Form





Sin[a (b z^n)^(1/n)] == (I/2) Sum[(((-I) a (b z^n)^(1/n))^i/i!) HypergeometricPFQ[{1}, {(i + 1)/n, (i + 2)/n, \[Ellipsis], (i + n)/n}, ((-I)^n a^n b z^n)/n^n] - ((I a (b z^n)^(1/n))^i/i!) HypergeometricPFQ[{1}, {(i + 1)/n, (i + 2)/n, \[Ellipsis], (i + n)/n}, (I^n a^n b z^n)/n^n], {i, 0, n - 1}] /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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</ci> <apply> <times /> <apply> <plus /> <ci> i </ci> <ci> n </ci> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </list> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> n </ci> </apply> <apply> <power /> <ci> a </ci> <ci> n </ci> </apply> <ci> b </ci> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <power /> <ci> n </ci> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> a </ci> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <ci> i </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> i </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> </list> <list> <apply> <times /> <apply> <plus /> <ci> i </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> i </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; 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Date Added to functions.wolfram.com (modification date)





2007-05-02