Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a89v)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a89v.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 17/4}, -z] == (Sqrt[Pi] (-814103915625 + 10131070950000 z - 19451656224000 z^2 + 57634536960000 z^3 + 23644938240000 z^4 + 1907490816000 z^5 + 44040192000 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(814103915625 - 1843492543200 z + 2574806572800 z^2 + 1375648727040 z^3 + 116699627520 z^4 + 2736783360 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (873126517725 - 1512898279200 z + 3367500998400 z^2 + 1456541614080 z^3 + 118708961280 z^4 + 2749366272 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/(50311515340800 z^(13/4))

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]