Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8319)

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`=3/2

http://functions.wolfram.com/07.22.03.8319.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 13/4}, -z] == (Sqrt[Pi] (-118587803709375 - 1011949258320000 z + 56669158465920000 z^2 + 120894204727296000 z^3 + 38379112611840000 z^4 + 3435333156864000 z^5 + 107775157862400 z^6 + 1234803097600 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(118587803709375 + 885455601030000 z + 5914514910124800 z^2 + 2219865590476800 z^3 + 208669400432640 z^4 + 6664586526720 z^5 + 76923535360 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-39529267903125 + 2729251425423600 z + 7179321175084800 z^2 + 2361011962982400 z^3 + 213476304814080 z^4 + 6721587118080 z^5 + 77124861952 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (78485963931648000 z^(9/4))

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]