Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.acg0)

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.acg0.01

Input Form

HypergeometricPFQ[{-(1/2), 6}, {-(11/2), -(9/2)}, z] == (1/147349125) (147349125 - 17860500 z - 1984500 z^2 - 907200 z^3 - 1360800 z^4 - 12700800 z^5 + 419126400 z^6 + 3022488000 z^7 + 4357261440 z^8 + 2494215360 z^9 + 708380640 z^10 + 110131080 z^11 + 9727200 z^12 + 482496 z^13 + 12416 z^14 + 128 z^15) + (1/147349125) (4 E^z Sqrt[Pi] (280816200 z^(13/2) + 1123264800 z^(15/2) + 1338006600 z^(17/2) + 700881300 z^(19/2) + 189782775 z^(21/2) + 28692090 z^(23/2) + 2490600 z^(25/2) + 122160 z^(27/2) + 3120 z^(29/2) + 32 z^(31/2)) 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]