Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ahb5)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.ahb5.01

Input Form

HypergeometricPFQ[{3/2, 6}, {-(11/2), 11/2}, -z] == (1/(5280 z^4)) (63504000 + 29332800 z + 9979200 z^2 + 2719080 z^3 + 613800 z^4 + 117900 z^5 + 19740 z^6 + 2975 z^7 + 444 z^8 + 104 z^9 + 144 z^10 - 16 z^11) + (1/(10560 z^(9/2))) ((Sqrt[Pi] (-63504000 - 71668800 z - 40824000 z^2 - 15661800 z^3 - 4548600 z^4 - 1064700 z^5 - 208740 z^6 - 35175 z^7 - 5190 z^8 - 680 z^9 - 80 z^10 - 304 z^11 + 32 z^12) 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]