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

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=5, a₂>=5

For fixed z and a₁=5, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(7/2), 1/2}, z] == (1/297675) (297675 - 4677750 z + 24324300 z^2 - 113513400 z^3 + 1102701600 z^4 + 3969725760 z^5 + 4009824000 z^6 + 1844519040 z^7 + 453859200 z^8 + 64060440 z^9 + 5300232 z^10 + 251760 z^11 + 6304 z^12 + 64 z^13) + (1/297675) (4 E^z Sqrt[Pi] (551350800 z^(9/2) + 1353315600 z^(11/2) + 1191380400 z^(13/2) + 511252560 z^(15/2) + 120881565 z^(17/2) + 16648065 z^(19/2) + 1355760 z^(21/2) + 63720 z^(23/2) + 1584 z^(25/2) + 16 z^(27/2)) 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]