Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aiu0)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=5/2, a₂=3, b₁=-11/2

http://functions.wolfram.com/07.25.03.aiu0.01

Input Form

HypergeometricPFQ[{5/2, 3}, {-(11/2), 11/2}, -z] == (1/(33 z^4)) (-127008000 - 31449600 z - 9192960 z^2 - 1975680 z^3 - 340863 z^4 - 48690 z^5 - 5880 z^6 - 608 z^7 - 54 z^8 - 4 z^9) + (1/(33 z^(9/2))) ((Sqrt[Pi] (63504000 + 58060800 z + 26369280 z^2 + 7922880 z^3 + 1769040 z^4 + 312480 z^5 + 45360 z^6 + 5544 z^7 + 579 z^8 + 52 z^9 + 4 z^10) Erfi[Sqrt[z]])/E^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]