Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2522)

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=5, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁=2

http://functions.wolfram.com/07.25.03.2522.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {2, 11/2}, -z] == (1/(805306368 z^4)) ((1091475 + 1351350 z + 1829520 z^2 + 10977120 z^3 + 567834144 z^4 + 898008384 z^5 + 420233472 z^6 + 78556672 z^7 + 6140672 z^8 + 165376 z^9)/E^z) + (1/(1610612736 z^(9/2))) (Sqrt[Pi] (-1091475 - 623700 z - 1122660 z^2 - 9979200 z^3 + 244490400 z^4 + 1760330880 z^5 + 2151515520 z^6 + 913296384 z^7 + 163088640 z^8 + 12446720 z^9 + 330752 z^10) 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]