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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=-9/2, b>=a > For fixed z and a=-9/2, b=-15/4





http://functions.wolfram.com/07.23.03.a9ym.01









  


  








Input Form





Hypergeometric2F1[-(9/2), -(15/4), 6, z] == (16 Sqrt[2] (2 (1 - z)^(1/4) (196608 - 4012032 z + 43374464 z^2 - 362638080 z^3 + 3404896320 z^4 + 71945289952 z^5 + 130896800472 z^6 + 58577851656 z^7 + 5978555010 z^8 + 46940355 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (196608 - 4012032 z + 43374464 z^2 - 362638080 z^3 + 3404896320 z^4 + 71945289952 z^5 + 130896800472 z^6 + 58577851656 z^7 + 5978555010 z^8 + 46940355 z^9) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (196608 - 4012032 z + 43374464 z^2 - 362638080 z^3 + 3404896320 z^4 + 71945289952 z^5 + 130896800472 z^6 + 58577851656 z^7 + 5978555010 z^8 + 46940355 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (196608 - 4012032 z + 43374464 z^2 - 362638080 z^3 + 3404896320 z^4 + 71945289952 z^5 + 130896800472 z^6 + 58577851656 z^7 + 5978555010 z^8 + 46940355 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (196608 - 4012032 z + 43374464 z^2 - 362638080 z^3 + 3404896320 z^4 + 71945289952 z^5 + 130896800472 z^6 + 58577851656 z^7 + 5978555010 z^8 + 46940355 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-196608 + 4110336 z - 45362048 z^2 + 383958400 z^3 - 3582331200 z^4 + 3638535008 z^5 + 104021681384 z^6 + 127522492128 z^7 + 36536121630 z^8 + 2048245695 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (591307651935 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3638535008 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 3582331200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 383958400 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 45362048 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4110336 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 196608 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 591307651935 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 15 <sep /> 4 </cn> </apply> </list> <list> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn 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Date Added to functions.wolfram.com (modification date)





2007-05-02