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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=21/4





http://functions.wolfram.com/07.23.03.a7ta.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 21/4, 6, z] == (1/(52190680647105 Pi z^5)) (16384 (-2 Sqrt[1 - z] (9844736 + 12152096 z + 21395957 z^2 + 58054139 z^3 + 313709627 z^4 - 10046155723 z^5 + 37245419552 z^6 - 60791719936 z^7 + 51771342848 z^8 - 22624075776 z^9 + 4026531840 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (9844736 + 4768544 z + 11589677 z^2 + 40835465 z^3 + 268081583 z^4 - 3915644413 z^5 + 12303493688 z^6 - 18187296256 z^7 + 14403829760 z^8 - 5939134464 z^9 + 1006632960 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (9844736 + 12152096 z + 21395957 z^2 + 58054139 z^3 + 313709627 z^4 - 10046155723 z^5 + 37245419552 z^6 - 60791719936 z^7 + 51771342848 z^8 - 22624075776 z^9 + 4026531840 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])]))










Standard Form





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MathML Form







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<cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21395957 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12152096 </cn> <ci> z </ci> </apply> <cn type='integer'> 9844736 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02