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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=5, b₁>=-11/2

For fixed z and a₁=3/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{3/2, 5}, {-(9/2), -(9/2)}, z] == (1/2679075) (2679075 + 992250 z + 607500 z^2 + 793800 z^3 + 3175200 z^4 + 125737920 z^5 + 3997468800 z^6 + 12614803200 z^7 + 13225075200 z^8 + 6384291840 z^9 + 1637725632 z^10 + 238970880 z^11 + 20287200 z^12 + 982592 z^13 + 24960 z^14 + 256 z^15) + (1/2679075) (16 E^z Sqrt[Pi] (45349200 z^(11/2) + 467445600 z^(13/2) + 1082450520 z^(15/2) + 988872480 z^(17/2) + 444062610 z^(19/2) + 109261620 z^(21/2) + 15540825 z^(23/2) + 1297896 z^(25/2) + 62184 z^(27/2) + 1568 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]