Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ul)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7ul.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(5/4)}, -z] == (1/(7725041280 z^(7/2))) (2 Sqrt[z] (-9820936125 + 137837700 z - 882161280 z^2 + 335784960 z^3 - 232783872 z^4 + 1490288640 z^5 + 137756672 z^6 + 2097152 z^7) Cos[2 Sqrt[z]] + 32768 Sqrt[Pi] z^(23/4) (184977 + 16864 z + 256 z^2) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (9820936125 - 13232419200 z - 2425943520 z^2 + 1069286400 z^3 - 489922560 z^4 + 696778752 z^5 + 68091904 z^6 + 1048576 z^7) Sin[2 Sqrt[z]])

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]