Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9539)

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/07.22.03.9539.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(15/4)}, -z] == (1/(1119242124000 z^(5/2))) (2 Sqrt[z] (-1031198293125 - 109994484600 z + 4410806400 z^2 - 276756480 z^3 + 30965760 z^4 - 7864320 z^5 + 8388608 z^6) Cos[2 Sqrt[z]] + 134217728 Sqrt[Pi] z^(29/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (1031198293125 - 1264936572900 z + 41902660800 z^2 - 2075673600 z^3 + 170311680 z^4 - 27525120 z^5 + 12582912 z^6 - 67108864 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]