Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8271)

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/07.22.03.8271.01

Input Form

HypergeometricPFQ[{-(23/4)}, {1/2, 13/4}, -z] == (Sqrt[Pi] (33204585038625 + 121433910998400 z + 2266766338636800 z^2 + 24178840945459200 z^3 + 13816480540262400 z^4 + 1786373241569280 z^5 + 73287107346432 z^6 + 1037234601984 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-33204585038625 - 86015686957200 z + 993206619175680 z^2 + 773770378752000 z^3 + 107584608337920 z^4 + 4520659648512 z^5 + 64575504384 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (11068195012875 + 35418224041200 z + 1385271984418560 z^2 + 844318451773440 z^3 + 110815402328064 z^4 + 4568399216640 z^5 + 64776830976 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (6278877114531840 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]