Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8881)

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`=3/2

http://functions.wolfram.com/07.22.03.8881.01

Input Form

HypergeometricPFQ[{-(21/4)}, {3/2, -(1/4)}, -z] == (1/(145363680 Sqrt[z])) ((-Sqrt[Pi]) z^(7/4) (3011753745 + 1946992320 z + 239629824 z^2 + 7913472 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 (4 Sqrt[z] (-10652040 + 170432640 z + 119071323 z^2 + 14885808 z^3 + 493824 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + (-15036840 + 115274880 z + 109336815 z^2 + 14528304 z^3 + 490752 z^4 + 4096 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]