Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ai2v)

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.ai2v.01

Input Form

HypergeometricPFQ[{2, 9/2}, {-(11/2), -(7/2)}, z] == (1/114604875) (114604875 + 53581500 z + 39293100 z^2 + 64864800 z^3 + 486486000 z^4 - 6616209600 z^5 + 97772875200 z^6 + 492712657920 z^7 + 608671445760 z^8 + 322176691200 z^9 + 88009804800 z^10 + 13471211520 z^11 + 1188982784 z^12 + 59523072 z^13 + 1556480 z^14 + 16384 z^15) + (1/114604875) (8192 E^z Sqrt[Pi] (27216000 z^(13/2) + 85881600 z^(15/2) + 90115200 z^(17/2) + 44029440 z^(19/2) + 11501280 z^(21/2) + 1713600 z^(23/2) + 148680 z^(25/2) + 7360 z^(27/2) + 191 z^(29/2) + 2 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]