Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ac4i)

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=5, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.ac4i.01

Input Form

HypergeometricPFQ[{-(1/2), 5}, {-(11/2), -(9/2)}, z] == (1/29469825) (29469825 - 2976750 z - 283500 z^2 - 113400 z^3 - 151200 z^4 - 1270080 z^5 + 38102400 z^6 + 243734400 z^7 + 308125440 z^8 + 151701120 z^9 + 36038592 z^10 + 4498800 z^11 + 299040 z^12 + 9920 z^13 + 128 z^14) + (1/29469825) (8 E^z Sqrt[Pi] (12209400 z^(13/2) + 43953840 z^(15/2) + 46299960 z^(17/2) + 20975220 z^(19/2) + 4768785 z^(21/2) + 580440 z^(23/2) + 37992 z^(25/2) + 1248 z^(27/2) + 16 z^(29/2)) 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]