Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8tv)

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

For fixed z and a₁=-11/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a8tv.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(11/2), 17/4}, -z] == (13 (Sqrt[Pi] (1996138596375 + 608347000800 z + 156992774400 z^2 + 124043673600 z^3 - 21572812800 z^4 + 1038090240 z^5 - 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(1996138596375 - 1520867502000 z + 48842196480 z^2 + 1412997120 z^3 - 65863680 z^4 + 1048576 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-665379532125 + 101391166800 z - 8789783040 z^2 + 1360896000 z^3 - 65077248 z^4 + 1048576 z^5) Sin[2 Sqrt[z]])))/ (1546188226560 z^(13/4))

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]