Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aba1)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.aba1.01

Input Form

HypergeometricPFQ[{-(1/4)}, {1/2, 23/4}, -z] == (1/(4294967296 z^(19/4))) (4389 (Sqrt[Pi] (-34459425 - 10810800 z - 2419200 z^2 - 614400 z^3 - 327680 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-11486475 + 1647360 z - 7680 z^2 - 32768 z^3 + 65536 z^4) Cos[2 Sqrt[z]] + (34459425 - 25945920 z + 222720 z^2 - 81920 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]