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

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=7/2, a₂>=7/2

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

For fixed z and a₁=7/2, a₂=6, b₁=-3/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(3/2), 11/2}, z] == (1/(640 z^4)) (7 (75600 - 30600 z + 9360 z^2 - 2340 z^3 + 570 z^4 - 315 z^5 + 1140 z^6 + 1192 z^7 + 272 z^8 + 16 z^9)) + (1/(1280 z^(9/2))) (7 E^z Sqrt[Pi] (-75600 + 81000 z - 43200 z^2 + 15300 z^3 - 4050 z^4 + 855 z^5 - 150 z^6 + 3240 z^7 + 2640 z^8 + 560 z^9 + 32 z^10) 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]