Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3788)

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=3

http://functions.wolfram.com/07.25.03.3788.01

Input Form

HypergeometricPFQ[{-(9/2), 1}, {3, 11/2}, -z] == -((18 (7 + 13 z))/(143 z^2)) + (1/(56229888 z^4)) ((-405405 + 2162160 z + 31599288 z^2 + 38391840 z^3 + 16653120 z^4 + 3305472 z^5 + 322176 z^6 + 14848 z^7 + 256 z^8)/E^z) + (1/(112459776 z^(9/2))) (Sqrt[Pi] (405405 - 2432430 z + 19459440 z^2 + 90810720 z^3 + 90810720 z^4 + 36324288 z^5 + 6918912 z^6 + 658944 z^7 + 29952 z^8 + 512 z^9) 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]