Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8941)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8941.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 11/4}, -z] == (Sqrt[Pi] (-25614965601225 + 318764016370800 z + 2185810397971200 z^2 + 1059786859622400 z^3 + 125604368547840 z^4 + 4881789222912 z^5 + 66588770304 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (8707129192125 + 126757534145760 z + 64879852988160 z^2 + 7794728976384 z^3 + 304338370560 z^4 + 4158652416 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-8875936517175 + 95396900770080 z + 59874855264000 z^2 + 7579040071680 z^3 + 301272072192 z^4 + 4146069504 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/(1714779743846400 z^(7/4))

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]