Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an7t)

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=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.an7t.01

Input Form

HypergeometricPFQ[{5, 5}, {-(11/2), 2}, z] == (1/5987520) (5987520 - 13608000 z + 18144000 z^2 - 21168000 z^3 + 27095040 z^4 - 48771072 z^5 + 232243200 z^6 + 313486065 z^7 + 136514052 z^8 + 28173708 z^9 + 3082464 z^10 + 182064 z^11 + 5440 z^12 + 64 z^13) + (1/11975040) (E^z Sqrt[Pi] (690136335 z^(13/2) + 741558258 z^(15/2) + 298527012 z^(17/2) + 59260824 z^(19/2) + 6341712 z^(21/2) + 369504 z^(23/2) + 10944 z^(25/2) + 128 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]