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

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=5, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 5}, {-(11/2), -(5/2)}, z] == (1/1403325) (1403325 + 1275750 z + 1984500 z^2 + 11907000 z^3 - 104781600 z^4 + 544864320 z^5 - 5448643200 z^6 - 19708358400 z^7 - 19605738240 z^8 - 8809920000 z^9 - 2109316608 z^10 - 289140480 z^11 - 23213280 z^12 - 1069632 z^13 - 25984 z^14 - 256 z^15) - (1/1403325) (16 E^z Sqrt[Pi] (683726400 z^(13/2) + 1675129680 z^(15/2) + 1451913120 z^(17/2) + 609038640 z^(19/2) + 140218920 z^(21/2) + 18765225 z^(23/2) + 1483464 z^(25/2) + 67656 z^(27/2) + 1632 z^(29/2) + 16 z^(31/2)) 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

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]