Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ac0j)

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`=-7/2

http://functions.wolfram.com/07.22.03.ac0j.01

Input Form

HypergeometricPFQ[{3/4}, {-(7/2), 19/4}, z] == (1/(268435456 z^(15/4))) ((33 (4 z^(1/4) (11658772125 + 15545029500 Sqrt[z] + 10681725600 z + 4767235200 z^(3/2) + 1447496960 z^2 + 293063680 z^(5/2) + 35651584 z^3 + 2097152 z^(7/2) + E^(4 Sqrt[z]) (-11658772125 + 15545029500 Sqrt[z] - 10681725600 z + 4767235200 z^(3/2) - 1447496960 z^2 + 293063680 z^(5/2) - 35651584 z^3 + 2097152 z^(7/2))) + 3315 E^(2 Sqrt[z]) Sqrt[2 Pi] (-3516975 + 529200 z - 48384 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] - 3315 E^(2 Sqrt[z]) Sqrt[2 Pi] (-3516975 + 529200 z - 48384 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]