Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vx)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7vx.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(5/4)}, -z] == (1/(120167308800 z^(9/2))) (2 Sqrt[z] (-1581170716125 + 366648282000 z + 23156733600 z^2 - 11762150400 z^3 + 3797606400 z^4 - 2477260800 z^5 + 15487467520 z^6 + 1244659712 z^7 + 16777216 z^8) Cos[2 Sqrt[z]] + 262144 Sqrt[Pi] z^(27/4) (239785 + 19040 z + 256 z^2) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (1581170716125 - 2474875903500 z - 96486390000 z^2 - 41167526400 z^3 + 12831436800 z^4 - 5339873280 z^5 + 7303331840 z^6 + 616038400 z^7 + 8388608 z^8) 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]