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

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=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(7/2), 5/2}, z] == (1/496125) (496125 - 1871100 z + 4864860 z^2 - 14414400 z^3 + 100245600 z^4 + 236862360 z^5 + 166861800 z^6 + 54486243 z^7 + 9492675 z^8 + 928040 z^9 + 50592 z^10 + 1424 z^11 + 16 z^12) + (1/992250) (E^z Sqrt[Pi] z^(9/2) (349188840 + 603144360 z + 380628045 z^2 + 117651135 z^3 + 19866210 z^4 + 1905288 z^5 + 102592 z^6 + 2864 z^7 + 32 z^8) 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]