Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ask6)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=3, a₃>=3

For fixed z and a₁=3/2, a₂=3, a₃=4

For fixed z and a₁=3/2, a₂=3, a₃=4, b₁=-7/2

http://functions.wolfram.com/07.27.03.ask6.01

Input Form

HypergeometricPFQ[{3/2, 3, 4}, {-(7/2), -(1/2)}, z] == (1/(896 (-1 + z)^12)) (896 - 1536 z - 235776 z^2 + 5490176 z^3 - 156535680 z^4 - 1765467024 z^5 - 3324478036 z^6 - 1612071171 z^7 - 173286414 z^8 - 840840 z^9) - (6435 (11440 z^(9/2) + 55900 z^(11/2) + 65665 z^(13/2) + 21492 z^(15/2) + 1512 z^(17/2)) ArcSin[Sqrt[z]])/(128 Sqrt[1 - z] (1 - 12 z + 66 z^2 - 220 z^3 + 495 z^4 - 792 z^5 + 924 z^6 - 792 z^7 + 495 z^8 - 220 z^9 + 66 z^10 - 12 z^11 + z^12))

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]