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

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=4, a₃>=4

For fixed z and a₁=-3/2, a₂=4, a₃=4

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

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

Input Form

HypergeometricPFQ[{-(3/2), 4, 4}, {-(7/2), -(7/2)}, z] == (1/(12544 (-1 + z)^13)) (-12544 + 187648 z - 1322496 z^2 + 5758464 z^3 - 21879552 z^4 - 466778664 z^5 - 3990714632 z^6 - 5475093619 z^7 - 1675889580 z^8 - 86630700 z^9) - (6435 (1144 z^(9/2) + 29640 z^(11/2) + 113865 z^(13/2) + 95422 z^(15/2) + 19320 z^(17/2) + 624 z^(19/2)) ArcSin[Sqrt[z]])/ (1792 Sqrt[1 - z] (-1 + 13 z - 78 z^2 + 286 z^3 - 715 z^4 + 1287 z^5 - 1716 z^6 + 1716 z^7 - 1287 z^8 + 715 z^9 - 286 z^10 + 78 z^11 - 13 z^12 + z^13))

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]