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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=6, b₁=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(5/2), 1/2}, -z] == (1/212625) (212625 + 5613300 z + 56756700 z^2 + 908107200 z^3 - 5513508000 z^4 + 8454045600 z^5 - 5653851840 z^6 + 1987359840 z^7 - 401133360 z^8 + 48440490 z^9 - 3525480 z^10 + 150224 z^11 - 3424 z^12 + 32 z^13) + (1/212625) ((Sqrt[Pi] (-2205403200 z^(7/2) + 8270262000 z^(9/2) - 10626033600 z^(11/2) + 6494115600 z^(13/2) - 2167489800 z^(15/2) + 423763515 z^(17/2) - 50132250 z^(19/2) + 3598920 z^(21/2) - 151920 z^(23/2) + 3440 z^(25/2) - 32 z^(27/2)) 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]