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

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=3/2

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

Input Form

HypergeometricPFQ[{-(3/4)}, {3/2, 21/4}, -z] == (1/(2684354560 z^(17/4))) (663 (Sqrt[Pi] (-2027025 - 1134000 z - 576000 z^2 - 614400 z^3 + 4915200 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((2027025 - 1028160 z - 84480 z^2 + 245760 z^3 + 65536 z^4) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-675675 - 69120 z - 69120 z^2 + 294912 z^3 + 65536 z^4) 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]