Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9519)

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`=5/2

http://functions.wolfram.com/07.22.03.9519.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 13/4}, -z] == (Sqrt[Pi] (1718663821875 - 38498069610000 z + 369581468256000 z^2 + 365018734080000 z^3 + 64179118080000 z^4 + 3294756864000 z^5 + 55784243200 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-1718663821875 + 11337450616800 z + 19707113260800 z^2 + 3830459351040 z^3 + 202715627520 z^4 + 3470786560 z^5 + 16777216 z^6)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-3051344609775 + 20041258960800 z + 22137702854400 z^2 + 3973971886080 z^3 + 205275463680 z^4 + 3483369472 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/ (408781062144000 z^(9/4))

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]