Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7859)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-3/4

http://functions.wolfram.com/07.22.03.7859.01

Input Form

HypergeometricPFQ[{6}, {-(3/4), 23/4}, -z] == (1/(67108864 z^(19/4))) (1463 (-4 z^(3/4) (12006225 - 4158000 z + 710640 z^2 - 87552 z^3 + 4096 z^4) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (36018675 - 26195400 z + 6456240 z^2 - 915840 z^3 + 122880 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + 3 (-12006225 + 24740100 z - 9525600 z^2 + 1696320 z^3 - 215040 z^4 + 16384 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((36018675 - 74220300 z + 28576800 z^2 - 5088960 z^3 + 645120 z^4 - 49152 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (36018675 - 26195400 z + 6456240 z^2 - 915840 z^3 + 122880 z^4 + 32768 z^5) Sin[2 Sqrt[z]])))

Standard Form

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MathML Form

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</semantics> </math>

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]