Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aaz2)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aaz2.01

Input Form

HypergeometricPFQ[{-(3/4)}, {9/2, 13/4}, z] == (1/(3620864 z^(7/2))) ((35 (4 (-2160 - 4320 Sqrt[z] + 10368 z - 3339 z^(3/2) + 9372 z^2 - 2208 z^(5/2) + 9600 z^3 + 256 z^(7/2) - 1024 z^4 + E^(4 Sqrt[z]) (2160 - 4320 Sqrt[z] - 10368 z - 3339 z^(3/2) - 9372 z^2 - 2208 z^(5/2) - 9600 z^3 + 256 z^(7/2) + 1024 z^4)) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-29835 - 31824 z - 39168 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-29835 - 31824 z - 39168 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]