Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9423)

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`=1/2

http://functions.wolfram.com/07.22.03.9423.01

Input Form

HypergeometricPFQ[{-(19/4)}, {1/2, 13/4}, -z] == (1/(9343567134720 z^(9/4))) (Sqrt[Pi] (68746552875 + 219988969200 z + 3519823507200 z^2 + 31287320064000 z^3 + 14302774886400 z^4 + 1386935746560 z^5 + 37933285376 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-68746552875 - 146659312800 z + 1367991555840 z^2 + 820855848960 z^3 + 84522762240 z^4 + 2355101696 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (22915517625 + 62853991200 z + 1817902759680 z^2 + 878600110080 z^3 + 86245834752 z^4 + 2367684608 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]