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

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=4, a₃>=4

For fixed z and a₁=7/2, a₂=4, a₃=4

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

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

Input Form

HypergeometricPFQ[{7/2, 4, 4}, {-(5/2), -(3/2)}, z] == (1/(3840 (-1 + z)^15)) (-3840 + 256 z - 3843840 z^2 + 1195649280 z^3 + 93186876160 z^4 + 1112759437440 z^5 + 4139802715776 z^6 + 5858352763120 z^7 + 3315884088660 z^8 + 714136912335 z^9 + 48711334980 z^10 + 624325548 z^11) + (3003 (219648 z^(7/2) + 6205056 z^(9/2) + 44047744 z^(11/2) + 112671952 z^(13/2) + 117163420 z^(15/2) + 50301669 z^(17/2) + 8283198 z^(19/2) + 423192 z^(21/2) + 3696 z^(23/2)) ArcSin[Sqrt[z]])/ (256 Sqrt[1 - z] (-1 + 15 z - 105 z^2 + 455 z^3 - 1365 z^4 + 3003 z^5 - 5005 z^6 + 6435 z^7 - 6435 z^8 + 5005 z^9 - 3003 z^10 + 1365 z^11 - 455 z^12 + 105 z^13 - 15 z^14 + z^15))

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]