Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3779)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=1, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=1, b₁=5/2

http://functions.wolfram.com/07.25.03.3779.01

Input Form

HypergeometricPFQ[{-(9/2), 1}, {5/2, 6}, -z] == -((3 (-120 + 456 z - 1292 z^2 + 6460 z^3 + 20995 z^4))/(46189 z^5)) + (1/(5542680 z^5)) ((-43200 + 120960 z - 322560 z^2 + 1935360 z^3 + 3441285 z^4 + 1721610 z^5 + 369528 z^6 + 37872 z^7 + 1808 z^8 + 32 z^9)/ E^z) + (1/(11085360 z^(3/2))) (Sqrt[Pi] (6235515 + 8314020 z + 3779100 z^2 + 775200 z^3 + 77520 z^4 + 3648 z^5 + 64 z^6) 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]