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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(9/2), -(9/2)}, z] == (1/40186125) (40186125 + 34728750 z + 38272500 z^2 + 78586200 z^3 + 454053600 z^4 + 24518894400 z^5 + 1064340950400 z^6 + 4601022854400 z^7 + 6657619772160 z^8 + 4513578324480 z^9 + 1672850242560 z^10 + 368040314880 z^11 + 50229473280 z^12 + 4328390656 z^13 + 233962368 z^14 + 7637248 z^15 + 136704 z^16 + 1024 z^17) + (1/40186125) (64 E^z Sqrt[Pi] (2539555200 z^(11/2) + 34381670400 z^(13/2) + 105879916800 z^(15/2) + 130892428800 z^(17/2) + 81453909600 z^(19/2) + 28691187840 z^(21/2) + 6113294880 z^(23/2) + 816962880 z^(25/2) + 69401865 z^(27/2) + 3714280 z^(29/2) + 120392 z^(31/2) + 2144 z^(33/2) + 16 z^(35/2)) Erf[Sqrt[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]