Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an7s)

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=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.an7s.01

Input Form

HypergeometricPFQ[{5, 5}, {-(11/2), 1}, -z] == (1/11975040) (11975040 + 54432000 z + 108864000 z^2 + 169344000 z^3 + 270950400 z^4 + 585252864 z^5 + 3251404800 z^6 - 5705913375 z^7 + 3198811194 z^8 - 862001172 z^9 + 127075032 z^10 - 10711248 z^11 + 510944 z^12 - 12736 z^13 + 128 z^14) + (1/23950080) ((Sqrt[Pi] (-10352045025 z^(13/2) + 13986763056 z^(15/2) - 7155129744 z^(17/2) + 1841531328 z^(19/2) - 264381024 z^(21/2) + 21921024 z^(23/2) - 1034496 z^(25/2) + 25600 z^(27/2) - 256 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]