Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8929)

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/07.22.03.8929.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(1/4)}, -z] == (1/(654136560 z^(3/2))) ((-Sqrt[Pi]) z^(11/4) (7392486465 + 3504586176 z + 340526592 z^2 + 9289728 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 (2 Sqrt[z] (13157235 - 70806960 z + 856687104 z^2 + 430547670 z^3 + 42351456 z^4 + 1159680 z^5 + 8192 z^6) Cos[2 Sqrt[z]] + (-13157235 - 75184200 z + 318245760 z^2 + 201092031 z^3 + 20753712 z^4 + 576768 z^5 + 4096 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]