Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9515)

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/07.22.03.9515.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 9/4}, -z] == (1/(8212119552000 z^(3/2))) (Sqrt[Pi] z^(1/4) (-343732764375 + 6599669076000 z + 9777287520000 z^2 + 2292111360000 z^3 + 147087360000 z^4 + 2988441600 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (149577449175 + 505101214800 z + 135293437440 z^2 + 9021726720 z^3 + 185794560 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + 4 (-24269414400 + 338451480675 z + 587548760400 z^2 + 141607226880 z^3 + 9158369280 z^4 + 186580992 z^5 + 1048576 z^6) 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]