Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ag3z)

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=1, a₃>=1

For fixed z and a₁=-3/2, a₂=1, a₃=2

For fixed z and a₁=-3/2, a₂=1, a₃=2, b₁=-7/2

http://functions.wolfram.com/07.27.03.ag3z.01

Input Form

HypergeometricPFQ[{-(3/2), 1, 2}, {-(7/2), -(7/2)}, z] == (2450 - 20200 z + 73544 z^2 - 155024 z^3 + 211948 z^4 - 11720 z^5 + 554832 z^6 + 19845 z^7)/(2450 (-1 + z)^8) + (99 (8 z^(9/2) + 88 z^(11/2) + 99 z^(13/2)) ArcSin[Sqrt[z]])/ (70 Sqrt[1 - z] (-1 + z)^8)

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]