Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5677)

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=-1/2, a₃>=-1/2

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

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

http://functions.wolfram.com/07.27.03.5677.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 4}, {7/2, 7/2}, z] == (-35385 + 495635 z + 11686992 z^2 + 2344104 z^3 - 421575 z^4 + 45045 z^5)/ (18874368 z^2) + (35 (-217 + 2646 z - 42525 z^2 + 20200 z^3 + 23625 z^4 - 4158 z^5 + 429 z^6) Log[1 - Sqrt[z]])/(12582912 z^(5/2)) - (35 (-217 + 2646 z - 42525 z^2 + 20200 z^3 + 23625 z^4 - 4158 z^5 + 429 z^6) Log[1 + Sqrt[z]])/(12582912 z^(5/2)) - (175 (1 - 18 z + 225 z^2 + 700 z^3) PolyLog[2, -Sqrt[z]])/ (524288 z^(5/2)) + (175 (1 - 18 z + 225 z^2 + 700 z^3) PolyLog[2, Sqrt[z]])/(524288 z^(5/2))

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]