Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9ol)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9ol.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 19/4}, -z] == (1/(263939162112 z^(9/2))) (7 (Sqrt[Pi] z^(3/4) (-141661448775 + 176616871200 z - 91749024000 z^2 + 43495833600 z^3 + 27471052800 z^4 + 1528823808 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-6967296000 + 11172093075 z - 5749878960 z^2 + 2433093120 z^3 + 1699454976 z^4 + 95354880 z^5 + 1048576 z^6) Cos[2 Sqrt[z]] + (13934592000 + 6296840775 z - 4546050480 z^2 + 1426982400 z^3 + 1631232000 z^4 + 94568448 z^5 + 1048576 z^6) 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]