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

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=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-7/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(7/2), -(1/2)}, z] == (1/33075) (33075 + 425250 z - 5613300 z^2 + 37837800 z^3 - 454053600 z^4 - 2009367360 z^5 - 2346489600 z^6 - 1210487040 z^7 - 327607680 z^8 - 50171840 z^9 - 4458552 z^10 - 225680 z^11 - 5984 z^12 - 64 z^13) - (1/33075) (4 E^z Sqrt[Pi] (245044800 z^(9/2) + 707288400 z^(11/2) + 708573600 z^(13/2) + 338464560 z^(15/2) + 87680040 z^(17/2) + 13073865 z^(19/2) + 1142120 z^(21/2) + 57160 z^(23/2) + 1504 z^(25/2) + 16 z^(27/2)) 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]