Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aeaj)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=6, b₁>=-11/2

For fixed z and a₁=1/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.aeaj.01

Input Form

HypergeometricPFQ[{1/2, 6}, {-(11/2), -(11/2)}, z] == (1/1620840375) (1620840375 + 160744500 z + 41674500 z^2 + 22680000 z^3 + 28576800 z^4 + 114307200 z^5 + 4610390400 z^6 + 151574976000 z^7 + 502023916800 z^8 + 560977079040 z^9 + 293931555840 z^10 + 83720508480 z^11 + 13978742400 z^12 + 1417076640 z^13 + 87571584 z^14 + 3198208 z^15 + 62976 z^16 + 512 z^17) + (1/1620840375) (16 E^z Sqrt[Pi] (1684897200 z^(13/2) + 17972236800 z^(15/2) + 43625622600 z^(17/2) + 42411070800 z^(19/2) + 20639483550 z^(21/2) + 5631083640 z^(23/2) + 915450795 z^(25/2) + 91208730 z^(27/2) + 5571240 z^(29/2) + 201840 z^(31/2) + 3952 z^(33/2) + 32 z^(35/2)) Erf[Sqrt[z]])

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,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},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]