Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a90n)

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

For fixed z and a₁=-11/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a90n.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(1/2), 21/4}, -z] == (221 (Sqrt[Pi] (44483063625 + 20170458000 z + 7171718400 z^2 + 3477196800 z^3 + 7947878400 z^4 - 8477736960 z^5 - 6459228160 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-44483063625 + 27278143200 z + 2292998400 z^2 + 56770560 z^3 - 213319680 z^4 - 387973120 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-14827687875 + 54885600 z - 412473600 z^2 - 473088000 z^3 + 461045760 z^4 + 400556032 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(2405181685760 z^(17/4))

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]