Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an1y)

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=-9/2

http://functions.wolfram.com/07.25.03.an1y.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), 3/2}, -z] == (1/1488375) (1488375 + 5953500 z + 13097700 z^2 + 25945920 z^3 + 64864800 z^4 + 400982400 z^5 - 815587920 z^6 + 512794800 z^7 - 152279946 z^8 + 24436650 z^9 - 2221320 z^10 + 113424 z^11 - 3008 z^12 + 32 z^13) - (1/1488375) ((Sqrt[Pi] z^(11/2) (666633240 - 1018263960 z + 579030795 z^2 - 163516185 z^3 + 25494210 z^4 - 2276568 z^5 + 114912 z^6 - 3024 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]