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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=-3/2, a2>=-3/2 > For fixed z and a1=-3/2, a2=1, a3>=1 > For fixed z and a1=-3/2, a2=1, a3=4 > For fixed z and a1=-3/2, a2=1, a3=4, b1=1/2





http://functions.wolfram.com/07.27.03.agj0.01









  


  








Input Form





HypergeometricPFQ[{-(3/2), 1, 4}, {1/2, 1/2}, -z] == (256 + 210 Pi^2 Sqrt[z] + 3988 z + 1365 Pi^2 z^(3/2) + 7560 z^2 + 2100 Pi^2 z^(5/2) + 3780 z^3 + 945 Pi^2 z^(7/2))/(256 (1 + z)^2) + (1/(1024 (1 + z)^(11/2))) ((-1024 - 40288 z - 239920 z^2 - 639264 z^3 - 913436 z^4 - 731533 z^5 - 310819 z^6 - 54744 z^7) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(1024 (1 + z)^(11/2))) ((1024 + 40288 z + 239920 z^2 + 639264 z^3 + 913436 z^4 + 731533 z^5 + 310819 z^6 + 54744 z^7) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + ((457 Sqrt[z] + 1939 z^(3/2) + 2415 z^(5/2) + 945 z^(7/2)) Log[Sqrt[z] + Sqrt[1 + z]])/(64 (1 + z)^(5/2)) + (1/(1024 (1 + z)^(11/2))) ((1024 + 40288 z + 239920 z^2 + 639264 z^3 + 913436 z^4 + 731533 z^5 + 310819 z^6 + 54744 z^7) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (105/64) (2 Sqrt[z] + 9 z^(3/2)) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] + (105/64) (2 Sqrt[z] + 9 z^(3/2)) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (105/64) (2 Sqrt[z] + 9 z^(3/2)) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]








Standard Form





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MathML Form







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





2007-05-02