Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an1s)

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.an1s.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(9/2), -(1/2)}, z] == (1/1488375) (1488375 + 17860500 z - 196465500 z^2 + 908107200 z^3 - 4086482400 z^4 + 39697257600 z^5 + 147294201600 z^6 + 157647772800 z^7 + 78804351360 z^8 + 21655294080 z^9 + 3528919800 z^10 + 352545480 z^11 + 21637600 z^12 + 789696 z^13 + 15616 z^14 + 128 z^15) + (1/1488375) (4 E^z Sqrt[Pi] (19998997200 z^(11/2) + 50766685200 z^(13/2) + 47348053200 z^(15/2) + 22055922000 z^(17/2) + 5816801025 z^(19/2) + 923822865 z^(21/2) + 90747090 z^(23/2) + 5506200 z^(25/2) + 199360 z^(27/2) + 3920 z^(29/2) + 32 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]