Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alq4)

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=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.alq4.01

Input Form

HypergeometricPFQ[{7/2, 6}, {-(7/2), -(5/2)}, z] == (1/354375) (354375 + 850500 z + 3572100 z^2 + 69854400 z^3 - 4086482400 z^4 - 53794540800 z^5 - 135621158400 z^6 - 134320144320 z^7 - 66565183680 z^8 - 18557681520 z^9 - 3095008560 z^10 - 317456520 z^11 - 20020192 z^12 - 750528 z^13 - 15232 z^14 - 128 z^15) - (1/354375) (4 E^z Sqrt[Pi] (3491888400 z^(9/2) + 23173441200 z^(11/2) + 45846297000 z^(13/2) + 40270671000 z^(15/2) + 18653868450 z^(17/2) + 4992082830 z^(19/2) + 811149315 z^(21/2) + 81777450 z^(23/2) + 5097000 z^(25/2) + 189520 z^(27/2) + 3824 z^(29/2) + 32 z^(31/2)) 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]