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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Continued fraction representations





http://functions.wolfram.com/07.24.10.0002.01









  


  








Input Form





Hypergeometric2F1Regularized[a, b, c, z] == (1/Gamma[c]) (1 + (a b z)/c/(1 + ContinueFraction[ {-(((a + k) (b + k) z)/((k + 1) (c + k))), 1 + ((a + k) (b + k) z)/((k + 1) (c + k))}, {k, 1, Infinity}]))








Standard Form





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MathML Form







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</ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> <apply> <plus /> <ci> b </ci> <ci> k </ci> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> c </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> k </ci> </apply> <apply> <plus /> <ci> b </ci> <ci> k </ci> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> c </ci> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <infinity /> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29