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

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, a₂>=5

For fixed z and a₁=5, a₂=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=-3/2

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

Input Form

HypergeometricPFQ[{5, 6}, {-(3/2), 1}, -z] == (1/552960) (552960 + 11059200 z + 232243200 z^2 - 1672706385 z^3 + 2740611780 z^4 - 1843407648 z^5 + 621191760 z^6 - 114724320 z^7 + 12007872 z^8 - 702976 z^9 + 21248 z^10 - 256 z^11) + (1/1105920) ((Sqrt[Pi] (-1217431215 z^(5/2) + 5118180210 z^(7/2) - 6905218320 z^(9/2) + 4217672160 z^(11/2) - 1346672160 z^(13/2) + 240804288 z^(15/2) - 24698112 z^(17/2) + 1426944 z^(19/2) - 42752 z^(21/2) + 512 z^(23/2)) 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]