Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8f9)

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`=-9/2

http://functions.wolfram.com/07.22.03.a8f9.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(9/2), 19/4}, -z] == -((11 (Sqrt[Pi] (135043557523875 + 41666331798000 z + 9852137568000 z^2 + 3502982246400 z^3 - 2668938854400 z^4 + 301433094144 z^5 - 13740539904 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (45014519174625 - 6689288642400 z + 260638560000 z^2 - 170735910912 z^3 + 19007471616 z^4 - 861929472 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-135043557523875 + 102380129560800 z - 1991278598400 z^2 - 188194406400 z^3 + 19706609664 z^4 - 874512384 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(51951924412416 z^(15/4)))

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]