Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8553)

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`=-11/2

http://functions.wolfram.com/07.22.03.8553.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 7/4}, -z] == (1/(5231974809600 z^(3/4))) (Sqrt[Pi] (-1090405850625 + 4187158466400 z - 1595107987200 z^2 + 222411571200 z^3 - 15792537600 z^4 + 660602880 z^5 - 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (-4 Sqrt[z] (-290528234325 + 102842686800 z - 14105387520 z^2 + 995205120 z^3 - 41484288 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (1090405850625 - 118283230800 z + 15013071360 z^2 - 1029611520 z^3 + 42270720 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]