Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1400)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=2, b₁=7/2

http://functions.wolfram.com/07.25.03.1400.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {7/2, 6}, -z] == (20 (24 - 126 z + 798 z^2 + 2261 z^3))/(29393 z^5) + (1/(1896201216 z^5)) ((-30965760 + 131604480 z - 882524160 z^2 - 1120857885 z^3 + 522140850 z^4 + 773002692 z^5 + 265816824 z^6 + 41019792 z^7 + 3159648 z^8 + 117440 z^9 + 1664 z^10)/E^z) + (1/(3792402432 z^(5/2))) (Sqrt[Pi] (-2749862115 - 2095133040 z + 1629547920 z^2 + 1777688640 z^3 + 569772000 z^4 + 85085952 z^5 + 6435072 z^6 + 236544 z^7 + 3328 z^8) 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]