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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=4, a₃>=4

For fixed z and a₁=5/2, a₂=4, a₃=4

For fixed z and a₁=5/2, a₂=4, a₃=4, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 4, 4}, {-(7/2), -(5/2)}, z] == (1/(5376 (-1 + z)^16)) (5376 - 61440 z + 538624 z^2 + 15994880 z^3 - 5863388160 z^4 - 476354848256 z^5 - 5976469222528 z^6 - 23638611943296 z^7 - 36121015495760 z^8 - 22554968147140 z^9 - 5531336469945 z^10 - 452522982912 z^11 - 7705565868 z^12) - (2145 (1098240 z^(9/2) + 32373120 z^(11/2) + 242072960 z^(13/2) + 660186096 z^(15/2) + 743687724 z^(17/2) + 353589379 z^(19/2) + 66617694 z^(21/2) + 4108104 z^(23/2) + 48048 z^(25/2)) ArcSin[Sqrt[z]])/ (256 Sqrt[1 - z] (1 - 16 z + 120 z^2 - 560 z^3 + 1820 z^4 - 4368 z^5 + 8008 z^6 - 11440 z^7 + 12870 z^8 - 11440 z^9 + 8008 z^10 - 4368 z^11 + 1820 z^12 - 560 z^13 + 120 z^14 - 16 z^15 + z^16))

Standard Form

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MathML Form

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</apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]