Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7003)

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=3

http://functions.wolfram.com/07.27.03.7003.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 2}, {3, 4}, z] == -((4 (-13860 - 168631 z - 239952 z^2 + 123440 z^3 - 37520 z^4 + 5040 z^5))/ (1486485 z^2)) + (1/(1486485 z^3)) (32 (1 - Sqrt[1 - z]) (-3465 - 63814 z + 40858 z^2 - 29994 z^3 + 15430 z^4 - 4690 z^5 + 630 z^6)) - (32 Log[(1/2) (1 + Sqrt[1 - z])])/(33 z^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]