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

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=6, a₂>=6

For fixed z and a₁=6, a₂=6, b₁>=-11/2

For fixed z and a₁=6, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{6, 6}, {-(9/2), 1}, z] == (1/217728000) (217728000 - 1741824000 z + 6096384000 z^2 - 17340825600 z^3 + 58525286400 z^4 - 468202291200 z^5 - 1397864237175 z^6 - 1273189410450 z^7 - 557691446880 z^8 - 136959994080 z^9 - 20235690720 z^10 - 1853353920 z^11 - 105210880 z^12 - 3577344 z^13 - 66304 z^14 - 512 z^15) + (1/435456000) (E^z Sqrt[Pi] (-1749495609225 z^(11/2) - 3726736209000 z^(13/2) - 3004393511700 z^(15/2) - 1235909203200 z^(17/2) - 292535056800 z^(19/2) - 42227877120 z^(21/2) - 3808502400 z^(23/2) - 213934080 z^(25/2) - 7220480 z^(27/2) - 133120 z^(29/2) - 1024 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]