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

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, a₂>=5

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

For fixed z and a₁=5, a₂=11/2, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(7/2), -(5/2)}, z] == (1/4465125) (4465125 + 14033250 z + 72972900 z^2 + 1702701000 z^3 - 115783668000 z^4 - 1792992801600 z^5 - 5287754908800 z^6 - 6136128794880 z^7 - 3585866630400 z^8 - 1192208140800 z^9 - 241221657600 z^10 - 30788997120 z^11 - 2511195648 z^12 - 129624000 z^13 - 4068480 z^14 - 70400 z^15 - 512 z^16) - (1/4465125) (32 E^z Sqrt[Pi] (13232419200 z^(9/2) + 101047564800 z^(11/2) + 230780793600 z^(13/2) + 235438358400 z^(15/2) + 127832191200 z^(17/2) + 40626411840 z^(19/2) + 7984539360 z^(21/2) + 999517320 z^(23/2) + 80439345 z^(25/2) + 4113240 z^(27/2) + 128232 z^(29/2) + 2208 z^(31/2) + 16 z^(33/2)) 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]