Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aj5b)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=4, b₁>=-11/2

For fixed z and a₁=5/2, a₂=4, b₁=-9/2

http://functions.wolfram.com/07.25.03.aj5b.01

Input Form

HypergeometricPFQ[{5/2, 4}, {-(9/2), -(5/2)}, z] == (1/127575) (127575 + 113400 z + 189000 z^2 + 1360800 z^3 - 17463600 z^4 + 242161920 z^5 + 1110170880 z^6 + 1229875200 z^7 + 571526400 z^8 + 133148160 z^9 + 16670592 z^10 + 1127296 z^11 + 38400 z^12 + 512 z^13) + (1/127575) (64 E^z Sqrt[Pi] (8353800 z^(11/2) + 24204600 z^(13/2) + 22897980 z^(15/2) + 9859500 z^(17/2) + 2202585 z^(19/2) + 268995 z^(21/2) + 17910 z^(23/2) + 604 z^(25/2) + 8 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]