Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajs9)

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=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.ajs9.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(9/2), -(3/2)}, -z] == (1/127575) (127575 - 283500 z + 1984500 z^2 + 19051200 z^3 + 104781600 z^4 + 1089728640 z^5 - 4117932000 z^6 + 4239079200 z^7 - 1960713360 z^8 + 481385520 z^9 - 67468716 z^10 + 5525280 z^11 - 259200 z^12 + 6400 z^13 - 64 z^14) + (1/127575) ((2 Sqrt[Pi] (-1111055400 z^(11/2) + 2820371400 z^(13/2) - 2521241100 z^(15/2) + 1086756300 z^(17/2) - 256326525 z^(19/2) + 35054730 z^(21/2) - 2825880 z^(23/2) + 131184 z^(25/2) - 3216 z^(27/2) + 32 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]