Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9571)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9571.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 17/4}, -z] == (Sqrt[Pi] (-448571257509375 + 6379680106800000 z - 14290483439232000 z^2 + 50810607783936000 z^3 + 26056721940480000 z^4 + 2802739838976000 z^5 + 97064583168000 z^6 + 1183263490048 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(448571257509375 - 1291334917395600 z + 2130749164051200 z^2 + 1484417395077120 z^3 + 169747999948800 z^4 + 5998195507200 z^5 + 73702309888 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (546328897173675 - 1118670295050000 z + 2928882227040000 z^2 + 1598009360855040 z^3 + 174063415787520 z^4 + 6052780179456 z^5 + 73903636480 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (46689086236262400 z^(13/4))

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]