Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8913)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8913.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(17/4)}, -z] == (1/(1084231348200 z^(3/2))) (-2 Sqrt[z] (316234143225 - 10475665200 z + 518918400 z^2 - 42577920 z^3 + 6881280 z^4 - 3145728 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] - 67108864 Sqrt[Pi] z^(27/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (316234143225 + 109994484600 z - 4410806400 z^2 + 276756480 z^3 - 30965760 z^4 + 7864320 z^5 - 8388608 z^6) Sin[2 Sqrt[z]])

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]