Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9615)

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`=9/2

http://functions.wolfram.com/07.22.03.9615.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 13/4}, -z] == (Sqrt[Pi] z^(5/4) (328952255506875 - 818725613706000 z + 3022986881376000 z^2 + 1580646735360000 z^3 + 172043182080000 z^4 + 6005871083520 z^5 + 73635201024 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (20386308096000 - 73443860703675 z + 125829045064800 z^2 + 89952383727360 z^3 + 10417227448320 z^4 + 371114311680 z^5 + 4586471424 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] + 4 (2548288512000 + 28540831334400 z - 64312410583575 z^2 + 174003011028000 z^3 + 96917088280320 z^4 + 10684162621440 z^5 + 374510911488 z^6 + 4599054336 z^7 + 16777216 z^8) Sin[2 Sqrt[z]]))/ (2794310546227200 z^(7/2))

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]