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

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, a₂>=5

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

For fixed z and a₁=5, a₂=11/2, b₁=-1/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(1/2), 1/2}, -z] == (1/2835) (2835 + 311850 z - 5613300 z^2 + 15966720 z^3 - 15966720 z^4 + 7333524 z^5 - 1746570 z^6 + 226875 z^7 - 16026 z^8 + 572 z^9 - 8 z^10) + (1/5670) ((Sqrt[Pi] (-2494800 z^(3/2) + 20207880 z^(5/2) - 43409520 z^(7/2) + 37962540 z^(9/2) - 16221870 z^(11/2) + 3705345 z^(13/2) - 469224 z^(15/2) + 32616 z^(17/2) - 1152 z^(19/2) + 16 z^(21/2)) Erfi[Sqrt[z]])/E^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]