Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an3s)

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=-3/2

http://functions.wolfram.com/07.25.03.an3s.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(3/2), -(1/2)}, z] == (1/4725) (4725 + 170100 z - 13097700 z^2 - 205405200 z^3 - 567567000 z^4 - 584503920 z^5 - 288958020 z^6 - 77322510 z^7 - 11874855 z^8 - 1065680 z^9 - 54672 z^10 - 1472 z^11 - 16 z^12) + (1/9450) (E^z Sqrt[Pi] (-97297200 z^(5/2) - 729729000 z^(7/2) - 1549548000 z^(9/2) - 1402537500 z^(11/2) - 645583050 z^(13/2) - 165577965 z^(15/2) - 24764250 z^(17/2) - 2184600 z^(19/2) - 110800 z^(21/2) - 2960 z^(23/2) - 32 z^(25/2)) 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]