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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=2, a3>=2 > For fixed z and a1=1/2, a2=2, a3=4 > For fixed z and a1=1/2, a2=2, a3=4, b1=7/2





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









  


  








Input Form





HypergeometricPFQ[{1/2, 2, 4}, {7/2, 7/2}, -z] == (75 (-24 Pi^2 + 232 Sqrt[z] - 24 Pi^2 z + 60 z^(3/2) + 15 Pi^2 z^2))/ (8192 z^(5/2)) + (1/(2048 z^2 (1 + z)^(13/2))) ((-1800 - 13200 z + 227941 z^2 - 254107 z^3 - 157013 z^4 - 125917 z^5 - 61298 z^6 - 16696 z^7 - 1950 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(2048 z^2 (1 + z)^(13/2))) ((1800 + 13200 z - 227941 z^2 + 254107 z^3 + 157013 z^4 + 125917 z^5 + 61298 z^6 + 16696 z^7 + 1950 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (75 Sqrt[1 + z] (-34 + 15 z) Log[Sqrt[z] + Sqrt[1 + z]])/(2048 z^(5/2)) + (1/(2048 z^2 (1 + z)^(13/2))) ((1800 + 13200 z - 227941 z^2 + 254107 z^3 + 157013 z^4 + 125917 z^5 + 61298 z^6 + 16696 z^7 + 1950 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225 (-8 - 8 z + 5 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (2048 z^(5/2)) + (225 (-8 - 8 z + 5 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(2048 z^(5/2)) - (225 (-8 - 8 z + 5 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (2048 z^(5/2))








Standard Form





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MathML Form







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





2007-05-02