Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj5e)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-9/2

http://functions.wolfram.com/07.25.03.aj5e.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(9/2), -(3/2)}, -z] == (1/25515) (25515 - 37800 z + 189000 z^2 + 1360800 z^3 + 5821200 z^4 + 48432384 z^5 - 133136640 z^6 + 98572800 z^7 - 31543296 z^8 + 5031168 z^9 - 414016 z^10 + 16640 z^11 - 256 z^12) + (1/25515) ((32 Sqrt[Pi] (-2784600 z^(11/2) + 5355000 z^(13/2) - 3508596 z^(15/2) + 1058484 z^(17/2) - 163443 z^(19/2) + 13194 z^(21/2) - 524 z^(23/2) + 8 z^(25/2)) 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]