Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9179)

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`=-9/2

http://functions.wolfram.com/07.22.03.9179.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 9/4}, -z] == (1/(570760888320 z^(5/4))) (Sqrt[Pi] (99687686175 + 416087733600 z - 291991392000 z^2 + 59325235200 z^3 - 5883494400 z^4 + 358612992 z^5 - 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(99687686175 + 24373757520 z - 4169894400 z^2 + 392601600 z^3 - 23396352 z^4 + 1048576 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-33229228725 + 19184815440 z - 3788628480 z^2 + 372350976 z^3 - 22609920 z^4 + 1048576 z^5) 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]