Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an21)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.an21.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), 5/2}, -z] == (1/496125) (496125 + 1190700 z + 1871100 z^2 + 2882880 z^3 + 5896800 z^4 + 30844800 z^5 - 48023640 z^6 + 23377410 z^7 - 5303319 z^8 + 630320 z^9 - 40080 z^10 + 1280 z^11 - 16 z^12) + (1/992250) ((Sqrt[Pi] z^(11/2) (-95233320 + 115378830 z - 51516885 z^2 + 11199930 z^3 - 1299480 z^4 + 81424 z^5 - 2576 z^6 + 32 z^7) 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]