Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9455)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.9455.01

Input Form

HypergeometricPFQ[{-(19/4)}, {3/2, -(3/4)}, -z] == (1/(3759210 Sqrt[z])) (-8 Sqrt[z] (-223020 + 685440 z + 288225 z^2 + 18912 z^3 + 256 z^4) Cos[2 Sqrt[z]] - 4 Sqrt[Pi] z^(9/4) (14549535 + 4883760 z + 306432 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (987525 - 2751840 z + 27498240 z^2 + 9655968 z^3 + 611328 z^4 + 8192 z^5) 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]