Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1017)

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=-7/2, a₃>=-7/2

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

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-7/2, b₁=-3/2

http://functions.wolfram.com/07.27.03.1017.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {-(3/2), 5/2}, z] == (245 (-z)^(5/2) (35 Pi^2 - 2 Pi^2 z))/4096 - (Sqrt[1 - z] (-15435 - 14452680 z - 145685836 z^2 - 623550688 z^3 + 144457184 z^4))/(15728640 z) - (1/(1048576 (-z)^(3/2))) (7 (-147 + 12250 z + 392000 z^2 + 2352000 z^3 + 4045440 z^4 - 713472 z^5) Log[Sqrt[1 - z] + Sqrt[-z]]) - (735 (35 - 2 z) (-z)^(5/2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/2048 + (735 (35 - 2 z) (-z)^(5/2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/1024 + (735 (35 - 2 z) (-z)^(5/2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/1024 - (735 (35 - 2 z) (-z)^(5/2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/1024

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]