Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an10)

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=-11/2

http://functions.wolfram.com/07.25.03.an10.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(11/2), -(1/2)}, z] == (1/16372125) (16372125 + 160744500 z - 1375258500 z^2 + 4540536000 z^3 - 12259447200 z^4 + 39697257600 z^5 - 307286179200 z^6 - 879076800000 z^7 - 772806182400 z^8 - 328034434560 z^9 - 78294686400 z^10 - 11268583200 z^11 - 1007265520 z^12 - 55895040 z^13 - 1860352 z^14 - 33792 z^15 - 256 z^16) - (1/16372125) (8 E^z Sqrt[Pi] (70765682400 z^(13/2) + 145462791600 z^(15/2) + 113515819200 z^(17/2) + 45323126100 z^(19/2) + 10435915350 z^(21/2) + 1468305405 z^(23/2) + 129290490 z^(25/2) + 7101080 z^(27/2) + 234640 z^(29/2) + 4240 z^(31/2) + 32 z^(33/2)) 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]