Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8921)

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/07.22.03.8921.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, -(9/4)}, -z] == (1/(4906024200 z^(3/2))) (-2 Sqrt[z] (723647925 - 330311520 z + 108138240 z^2 - 71221248 z^3 + 447283200 z^4 + 37060608 z^5 + 524288 z^6) Cos[2 Sqrt[z]] - 8192 Sqrt[Pi] z^(19/4) (221697 + 18144 z + 256 z^2) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (723647925 + 1157836680 z - 362880000 z^2 + 152893440 z^3 - 210567168 z^4 - 18333696 z^5 - 262144 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]