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

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.acga.01

Input Form

HypergeometricPFQ[{-(1/2), 6}, {-(11/2), 1/2}, z] == (1/623700) (623700 - 567000 z + 239400 z^2 - 44100 z^3 - 22140 z^4 + 47985 z^5 - 160335 z^6 - 78000 z^7 - 12112 z^8 - 752 z^9 - 16 z^10) + (1/1247400) (E^z Sqrt[Pi] (1247400 Sqrt[z] - 1247400 z^(3/2) + 623700 z^(5/2) - 207900 z^(7/2) + 51975 z^(9/2) - 10395 z^(11/2) - 388290 z^(13/2) - 167400 z^(15/2) - 24960 z^(17/2) - 1520 z^(19/2) - 32 z^(21/2)) 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]