Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8199)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8199.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), -(11/4)}, -z] == (1/2297295) ((2297295 + 5012280 z - 3379200 z^2 + 5490688 z^3 + 785408 z^4 + 16384 z^5) Cos[2 Sqrt[z]] + 512 Sqrt[Pi] z^(15/4) (96577 + 12512 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 Sqrt[z] (-2297295 + 2019360 z - 1744128 z^2 + 12075008 z^3 + 1595392 z^4 + 32768 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]