Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a99x)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a99x.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(11/2), 19/4}, -z] == (1/(412316860416 z^(15/4))) (13 Sqrt[Pi] (-3285083253375 - 774859932000 z - 134174880000 z^2 - 32901120000 z^3 + 15792537600 z^4 - 962592768 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (52 Sqrt[z] (-1095027751125 + 242297470800 z - 7553548800 z^2 + 998744064 z^3 - 60358656 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (42706082293875 - 35479975330800 z + 2568604147200 z^2 + 1535385600 z^3 - 794886144 z^4 + 13631488 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]