Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6891)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-15/4

http://functions.wolfram.com/07.22.03.6891.01

Input Form

HypergeometricPFQ[{3}, {-(15/4), 19/4}, -z] == (1/(4096 z^(15/4))) (-4 z^(3/4) (52026975 - 12972960 z + 1330560 z^2 - 56320 z^3 + 512 z^4) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-156080925 + 306486180 z - 92640240 z^2 + 9959040 z^3 - 435456 z^4 + 4096 z^5) Cos[2 Sqrt[z]] - 14 Sqrt[z] (22297275 - 14054040 z + 2423520 z^2 - 168192 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (14 Sqrt[z] (22297275 - 14054040 z + 2423520 z^2 - 168192 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + (-156080925 + 306486180 z - 92640240 z^2 + 9959040 z^3 - 435456 z^4 + 4096 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]