Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a81v)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.a81v.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(5/2), 17/4}, -z] == (13 (Sqrt[Pi] (236102414625 + 127746234000 z + 64545465600 z^2 + 114747494400 z^3 - 55635148800 z^4 + 10899947520 z^5 - 1761607680 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-236102414625 + 124096341600 z + 7757164800 z^2 - 3968778240 z^3 + 722534400 z^4 - 94371840 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-78700804875 - 6604567200 z - 7863609600 z^2 + 3607511040 z^3 - 695009280 z^4 + 106954752 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(1803886264320 z^(13/4))

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]