Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6898)

HypergeometricPFQ

$Mathematica Notation$

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=2

For fixed z and a₁=-7/2, a₂=1, a₃=2, b₁=-5/2

http://functions.wolfram.com/07.27.03.6898.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 2}, {-(5/2), 3/2}, -z] == (2880 - 4704 z + 9800 z^2 - 44100 z^3 - 11025 Pi^2 z^(7/2))/5120 + (1/(491520 (1 + z)^(15/2))) ((-491520 - 2335456 z - 4872720 z^2 + 1042100 z^3 + 61739810 z^4 + 294662865 z^5 + 698707709 z^6 + 987173985 z^7 + 869530305 z^8 + 470669850 z^9 + 143871000 z^10 + 19073040 z^11) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(491520 (1 + z)^(15/2))) ((491520 + 2335456 z + 4872720 z^2 - 1042100 z^3 - 61739810 z^4 - 294662865 z^5 - 698707709 z^6 - 987173985 z^7 - 869530305 z^8 - 470669850 z^9 - 143871000 z^10 - 19073040 z^11) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (7 (-16 + 24 z - 42 z^2 + 105 z^3 + 315 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/ (256 Sqrt[z] Sqrt[1 + z]) + (1/(491520 (1 + z)^(15/2))) ((491520 + 2335456 z + 4872720 z^2 - 1042100 z^3 - 61739810 z^4 - 294662865 z^5 - 698707709 z^6 - 987173985 z^7 - 869530305 z^8 - 470669850 z^9 - 143871000 z^10 - 19073040 z^11) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (2205/256) z^(7/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] - (2205/256) z^(7/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] + (2205/256) z^(7/2) 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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]