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

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=-3/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(3/2), -(3/2)}, z] == (1/25515) (25515 + 311850 z + 24324300 z^2 + 1339458120 z^3 + 6758912160 z^4 + 10772745984 z^5 + 7699648320 z^6 + 2896574160 z^7 + 623236176 z^8 + 79834968 z^9 + 6134408 z^10 + 274800 z^11 + 6560 z^12 + 64 z^13) + (1/25515) (4 E^z Sqrt[Pi] (45405360 z^(5/2) + 732972240 z^(7/2) + 2552429880 z^(9/2) + 3422404440 z^(11/2) + 2228255190 z^(13/2) + 793702098 z^(15/2) + 165100257 z^(17/2) + 20693169 z^(19/2) + 1567152 z^(21/2) + 69512 z^(23/2) + 1648 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]