Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9037)

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`=9/2

http://functions.wolfram.com/07.22.03.9037.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 11/4}, -z] == (Sqrt[Pi] z^(7/4) (-1323439889396625 + 4491674776134000 z + 14373359283628800 z^2 + 4034627167334400 z^3 + 311855239987200 z^4 + 8529374085120 z^5 + 86318776320 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-12125707776000 - 48502831104000 z + 179689608332325 z^2 + 857852005500000 z^3 + 248715120326400 z^4 + 19393169080320 z^5 + 532081213440 z^6 + 5391777792 z^7 + 16777216 z^8) Cos[2 Sqrt[z]] + (24251415552000 + 64670441472000 z - 56196195339375 z^2 + 718909215242400 z^3 + 235690099142400 z^4 + 19010545827840 z^5 + 528090071040 z^6 + 5379194880 z^7 + 16777216 z^8) Sin[2 Sqrt[z]]))/ (13289543014809600 z^(7/2))

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]