Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ach6)

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=-9/2

http://functions.wolfram.com/07.25.03.ach6.01

Input Form

HypergeometricPFQ[{-(1/2), 6}, {-(9/2), 3/2}, -z] == (1/226800) (113400 + 110880 z + 51660 z^2 + 13032 z^3 - 2265 z^4 - 18480 z^5 + 5712 z^6 - 544 z^7 + 16 z^8) + (1/(453600 Sqrt[z])) ((Sqrt[Pi] (113400 - 136080 z - 192780 z^2 - 105840 z^3 - 36855 z^4 - 9450 z^5 + 42168 z^6 - 11952 z^7 + 1104 z^8 - 32 z^9) Erfi[Sqrt[z]])/E^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]