Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akm8)

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=3, a₂>=3

For fixed z and a₁=3, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.akm8.01

Input Form

HypergeometricPFQ[{3, 11/2}, {-(11/2), -(1/2)}, -z] == (1/9823275) (9823275 - 58939650 z - 340540200 z^2 - 810810000 z^3 - 1654052400 z^4 - 4190266080 z^5 - 26072766720 z^6 + 53324490240 z^7 - 33563255040 z^8 + 9954362880 z^9 - 1593022464 z^10 + 144267264 z^11 - 7333888 z^12 + 193536 z^13 - 2048 z^14) + (1/9823275) ((512 Sqrt[Pi] (84823200 z^(13/2) - 130062240 z^(15/2) + 74012400 z^(17/2) - 20873160 z^(19/2) + 3245550 z^(21/2) - 288750 z^(23/2) + 14511 z^(25/2) - 380 z^(27/2) + 4 z^(29/2)) 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]