Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8jd)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a8jd.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(3/2), 23/4}, -z] == (209 (Sqrt[Pi] (-31750052709375 - 10837351324800 z - 2627236684800 z^2 - 706483814400 z^3 - 362299392000 z^4 + 515270246400 z^5 - 164886478848 z^6 + 83751862272 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-10583350903125 + 1225652828400 z - 6255325440 z^2 - 37890478080 z^3 + 35602366464 z^4 - 11176771584 z^5 + 5184159744 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (31750052709375 - 23029371565200 z - 331532248320 z^2 - 122427002880 z^3 + 52332134400 z^4 - 14221836288 z^5 + 4982833152 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (158329674399744 z^(19/4))

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]