Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ai2r)

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=2, a₂>=2

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

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

http://functions.wolfram.com/07.25.03.ai2r.01

Input Form

HypergeometricPFQ[{2, 9/2}, {-(11/2), -(11/2)}, z] == (1/11345882625) (11345882625 + 3375634500 z + 1375258500 z^2 + 972972000 z^3 + 1459458000 z^4 + 6616209600 z^5 + 293318625600 z^6 + 10512038476800 z^7 + 37673239968000 z^8 + 45258011366400 z^9 + 25372054103040 z^10 + 7703190282240 z^11 + 1366767390720 z^12 + 146844794880 z^13 + 9595207680 z^14 + 369754112 z^15 + 7667712 z^16 + 65536 z^17) + (1/11345882625) (32768 E^z Sqrt[Pi] (54432000 z^(13/2) + 624153600 z^(15/2) + 1623888000 z^(17/2) + 1687392000 z^(19/2) + 875448000 z^(21/2) + 254016000 z^(23/2) + 43817760 z^(25/2) + 4622400 z^(27/2) + 298350 z^(29/2) + 11400 z^(31/2) + 235 z^(33/2) + 2 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]