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

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, a₂>=3

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

For fixed z and a₁=3, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3, 11/2}, {-(9/2), -(7/2)}, -z] == (1/93767625) (93767625 - 98232750 z + 145945800 z^2 - 486486000 z^3 + 8270262000 z^4 + 439977938400 z^5 - 5314526380800 z^6 + 12502358346240 z^7 - 11674303200000 z^8 + 5494550284800 z^9 - 1462797527040 z^10 + 233972674560 z^11 - 23096414208 z^12 + 1405870080 z^13 - 50995200 z^14 + 1003520 z^15 - 8192 z^16) + (1/93767625) ((2048 Sqrt[Pi] (-707616000 z^(11/2) + 4381776000 z^(13/2) - 8157542400 z^(15/2) + 6787670400 z^(17/2) - 2994304320 z^(19/2) + 766493280 z^(21/2) - 119568960 z^(23/2) + 11608920 z^(25/2) - 698670 z^(27/2) + 25143 z^(29/2) - 492 z^(31/2) + 4 z^(33/2)) 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]