Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9093)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9093.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 19/4}, -z] == (Sqrt[Pi] z^(3/4) (-27820029915006454125 + 52027068931960122000 z - 43243278073317504000 z^2 + 35875904771937484800 z^3 + 45316932343499980800 z^4 + 6304964499965214720 z^5 + 276761130313973760 z^6 + 4709157835898880 z^7 + 31658203938816 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-1043004880060416000 + 3044047659520856625 z - 2576380733792611200 z^2 + 1836862909812403200 z^3 + 2764828249235619840 z^4 + 390932816282910720 z^5 + 17243185851924480 z^6 + 293953131773952 z^7 + 1977832439808 z^8 + 4294967296 z^9) Cos[2 Sqrt[z]] + (2086009760120832000 + 403901639132662125 z - 1281124565403883200 z^2 + 601747814220134400 z^3 + 2518002919950336000 z^4 + 378867251413647360 z^5 + 17028805684101120 z^6 + 292483246325760 z^7 + 1974611214336 z^8 + 4294967296 z^9) Sin[2 Sqrt[z]]))/ (51464842651096842240 z^(9/2))

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]