Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an1n)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.an1n.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), -(7/2)}, -z] == (1/156279375) (156279375 - 267907500 z + 589396500 z^2 - 2724321600 z^3 + 61297236000 z^4 + 4168212048000 z^5 - 66076686748800 z^6 + 203115969100800 z^7 - 249479417214720 z^8 + 156638079360000 z^9 - 56859265612800 z^10 + 12796650639360 z^11 - 1858981447680 z^12 + 177844972032 z^13 - 11235161280 z^14 + 461012480 z^15 - 11747328 z^16 + 167936 z^17 - 1024 z^18) + (1/156279375) ((32 Sqrt[Pi] (-479975932800 z^(11/2) + 3765965011200 z^(13/2) - 8967755462400 z^(15/2) + 9674567683200 z^(17/2) - 5636522959200 z^(19/2) + 1953351711360 z^(21/2) - 426542790240 z^(23/2) + 60712870680 z^(25/2) - 5726436765 z^(27/2) + 358124970 z^(29/2) - 14587608 z^(31/2) + 369712 z^(33/2) - 5264 z^(35/2) + 32 z^(37/2)) 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]