Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acv6)

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.acv6.01

Input Form

HypergeometricPFQ[{7/4}, {-(9/2), 19/4}, z] == -((1/(1207959552 z^(15/4))) ((11 (4 z^(1/4) (1154218440375 + 1538957920500 Sqrt[z] + 1129417052400 z + 567857908800 z^(3/2) + 208154419200 z^2 + 57028608000 z^(5/2) + 11698176000 z^3 + 1736441856 z^(7/2) + 169869312 z^4 + 8388608 z^(9/2) + E^(4 Sqrt[z]) (-1154218440375 + 1538957920500 Sqrt[z] - 1129417052400 z + 567857908800 z^(3/2) - 208154419200 z^2 + 57028608000 z^(5/2) - 11698176000 z^3 + 1736441856 z^(7/2) - 169869312 z^4 + 8388608 z^(9/2))) - 15663375 E^(2 Sqrt[z]) Sqrt[2 Pi] (73689 - 6496 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 15663375 E^(2 Sqrt[z]) Sqrt[2 Pi] (73689 - 6496 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

Standard Form

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MathML Form

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</semantics> </math>

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]