Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.abt0)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=4, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.abt0.01

Input Form

HypergeometricPFQ[{-(1/2), 4}, {-(11/2), -(11/2)}, z] == (1/324168075) (324168075 - 21432600 z - 1323000 z^2 - 324000 z^3 - 226800 z^4 - 564480 z^5 - 15240960 z^6 - 330163200 z^7 - 702071040 z^8 - 486051840 z^9 - 149188608 z^10 - 22889216 z^11 - 1808640 z^12 - 69632 z^13 - 1024 z^14) - (1/324168075) (128 E^z Sqrt[Pi] (581400 z^(13/2) + 4302360 z^(15/2) + 6969960 z^(17/2) + 4305960 z^(19/2) + 1248525 z^(21/2) + 185625 z^(23/2) + 14398 z^(25/2) + 548 z^(27/2) + 8 z^(29/2)) 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]