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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {-(11/2), 21/4}, -z] == (221 (-1463 Sqrt[Pi] (-46117214325 - 7276878000 z - 739238400 z^2 - 76308480 z^3 - 22609920 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (-5 (13493896911495 - 12264275536128 z + 1600628553216 z^2 - 40596111360 z^3 + 126550016 z^4) Cos[2 Sqrt[z]] + 76 Sqrt[z] (-1183675167675 + 354335446080 z - 21043653120 z^2 + 91570176 z^3 + 5046272 z^4) Sin[2 Sqrt[z]])))/(5291399708672 z^(17/4))

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]