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

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=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-9/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(9/2), 11/2}, z] == (1/(1440 z^4)) (-19051200 + 8164800 z - 2623320 z^2 + 672840 z^3 - 141300 z^4 + 24660 z^5 - 3465 z^6 + 231 z^7 + 228 z^8 - 792 z^9 - 256 z^10 - 16 z^11) + (1/(2880 z^(9/2))) (E^z Sqrt[Pi] (19051200 - 20865600 z + 11453400 z^2 - 4195800 z^3 + 1152900 z^4 - 253260 z^5 + 46305 z^6 - 7245 z^7 + 990 z^8 - 120 z^9 - 1824 z^10 - 528 z^11 - 32 z^12) 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

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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]
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