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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=1/2, a2>=1/2 > For fixed z and a1=1/2, a2=1, a3>=1 > For fixed z and a1=1/2, a2=1, a3=4 > For fixed z and a1=1/2, a2=1, a3=4, b1=7/2





http://functions.wolfram.com/07.27.03.angk.01









  


  








Input Form





HypergeometricPFQ[{1/2, 1, 4}, {7/2, 7/2}, -z] == (25 (72 Pi^2 - 792 Sqrt[z] + 216 Pi^2 z - 1508 z^(3/2) + 135 Pi^2 z^2))/ (12288 z^(5/2)) + (1/(9216 z^2 (1 + z)^(11/2))) ((5400 + 45000 z + 219557 z^2 + 374480 z^3 + 435933 z^4 + 297409 z^5 + 111574 z^6 + 17775 z^7) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(9216 z^2 (1 + z)^(11/2))) ((-5400 - 45000 z - 219557 z^2 - 374480 z^3 - 435933 z^4 - 297409 z^5 - 111574 z^6 - 17775 z^7) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (75 Sqrt[1 + z] (14 + 15 z) Log[Sqrt[z] + Sqrt[1 + z]])/(1024 z^(5/2)) + (1/(9216 z^2 (1 + z)^(11/2))) ((-5400 - 45000 z - 219557 z^2 - 374480 z^3 - 435933 z^4 - 297409 z^5 - 111574 z^6 - 17775 z^7) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (75 (8 + 24 z + 15 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (1024 z^(5/2)) + (75 (8 + 24 z + 15 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(1024 z^(5/2)) - (75 (8 + 24 z + 15 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (1024 z^(5/2))








Standard Form





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MathML Form







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Rule Form





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





2007-05-02