Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9xz)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a9xz.01

Input Form

HypergeometricPFQ[{-(7/4)}, {1/2, 21/4}, -z] == (1/(42949672960 z^(17/4))) (221 (Sqrt[Pi] (212837625 + 104781600 z + 42336000 z^2 + 25804800 z^3 + 103219200 z^4 + 220200960 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-212837625 + 122245200 z + 11773440 z^2 - 2580480 z^3 + 12779520 z^4 + 1048576 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (70945875 + 2494800 z + 3386880 z^2 + 4300800 z^3 + 13565952 z^4 + 1048576 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]