Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2960)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.2960.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 2}, {1/2, 7/2}, z] == (105 - 490 z + 60132 z^2 + 391020 z^3 + 199395 z^4 + 3150 z^5)/(65536 z^2) + (105 (1 - 5 z - 50 z^2 - 1300 z^3 + 275 z^4 + 1049 z^5 + 30 z^6) Log[1 - Sqrt[z]])/(131072 z^(5/2)) - (105 (1 - 5 z - 50 z^2 - 1300 z^3 + 275 z^4 + 1049 z^5 + 30 z^6) Log[1 + Sqrt[z]])/(131072 z^(5/2)) - (1575 Sqrt[z] (10 + 25 z + 7 z^2) PolyLog[2, -Sqrt[z]])/16384 + (1575 Sqrt[z] (10 + 25 z + 7 z^2) PolyLog[2, Sqrt[z]])/16384

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

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]