Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5687)

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=1

http://functions.wolfram.com/07.25.03.5687.01

Input Form

HypergeometricPFQ[{-(9/2), 6}, {1, 11/2}, -z] == (1/(805306368 z^4)) ((-694575 - 1228500 z - 1920240 z^2 - 5518800 z^3 + 681923616 z^4 + 2036823360 z^5 + 1203121920 z^6 + 220929280 z^7 + 11824384 z^8)/E^z) + (1/(1610612736 z^(9/2))) (Sqrt[Pi] (694575 + 765450 z + 1224720 z^2 + 4445280 z^3 + 120022560 z^4 + 2640496320 z^5 + 5085400320 z^6 + 2615348736 z^7 + 453682944 z^8 + 23648768 z^9) 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]