Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2169)

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=4, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁=5

http://functions.wolfram.com/07.25.03.2169.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {5, 11/2}, -z] == 1512/(4199 z^4) + (1/(33022279680 z^4)) ((-7307748315 + 4259132010 z - 3850292880 z^2 + 5001968160 z^3 + 16142665440 z^4 + 8136324288 z^5 + 1644273408 z^6 + 156236288 z^7 + 6898944 z^8 + 113152 z^9)/E^z) + (1/(66044559360 z^(9/2))) (Sqrt[Pi] (-4583103525 - 13094581500 z + 7856748900 z^2 - 8380532160 z^3 + 20951330400 z^4 + 39109150080 z^5 + 17776886400 z^6 + 3438167040 z^7 + 319258368 z^8 + 13911040 z^9 + 226304 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]