Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an16)

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=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.an16.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(11/2), 3/2}, -z] == (1/16372125) (16372125 + 53581500 z + 91683900 z^2 + 129729600 z^3 + 194594400 z^4 + 400982400 z^5 + 2148854400 z^6 - 3574912320 z^7 + 1919461320 z^8 - 498088920 z^9 + 70980300 z^10 - 5800800 z^11 + 268928 z^12 - 6528 z^13 + 64 z^14) - (1/16372125) ((2 Sqrt[Pi] z^(13/2) (1684897200 - 2176325550 z + 1069579350 z^2 - 265493025 z^3 + 36877050 z^4 - 2966040 z^5 + 136080 z^6 - 3280 z^7 + 32 z^8) 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]