Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8kl)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a8kl.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(1/2), 19/4}, -z] == -((1/(360777252864 z^(15/4))) (11 (Sqrt[Pi] (28222269075 + 16903177200 z + 8915961600 z^2 + 8805888000 z^3 - 28178841600 z^4 + 54103375872 z^5 + 10687086592 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (9407423025 + 1333856160 z + 1091301120 z^2 - 2163818496 z^3 + 3263102976 z^4 + 664797184 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-28222269075 + 13200576480 z + 1468696320 z^2 - 3019161600 z^3 + 2817196032 z^4 + 652214272 z^5 + 16777216 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]