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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Specific values > For rational parameters with larger denominators and fixed z > For fixed z and a1=4, b1>=-23/4 > For fixed z and a1=4, b1=-21/4





http://functions.wolfram.com/07.22.03.7120.01









  


  










Input Form





HypergeometricPFQ[{4}, {-(21/4), 21/4}, z] == (1/(4128768 z^(17/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (383016508875 + 150105255300 z + 27070243200 z^2 + 2361078720 z^3 + 114741504 z^4 + 2868224 z^5 + 16384 z^6) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-383016508875 + 766033017750 Sqrt[z] - 762931669500 z + 504485982000 z^(3/2) - 249080832000 z^2 + 97880983200 z^(5/2) - 31852941120 z^3 + 8811728640 z^(7/2) - 2106466560 z^4 + 437184000 z^(9/2) - 77552640 z^5 + 11169792 z^(11/2) - 1163264 z^6 + 65536 z^(13/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (383016508875 + 766033017750 Sqrt[z] + 762931669500 z + 504485982000 z^(3/2) + 249080832000 z^2 + 97880983200 z^(5/2) + 31852941120 z^3 + 8811728640 z^(7/2) + 2106466560 z^4 + 437184000 z^(9/2) + 77552640 z^5 + 11169792 z^(11/2) + 1163264 z^6 + 65536 z^(13/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))










Standard Form





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MathML Form







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<cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 383016508875 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </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