Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a93b)

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

For fixed z and a₁=-11/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a93b.01

Input Form

HypergeometricPFQ[{-(11/4)}, {3/2, 21/4}, -z] == (17 (Sqrt[Pi] (-18261468225 - 14302688400 z - 10897286400 z^2 - 19372953600 z^3 + 309967257600 z^4 + 198379044864 z^5 + 16793993216 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((18261468225 - 5176211040 z + 588107520 z^2 + 11070259200 z^3 + 11476598784 z^4 + 1033895936 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-6087156075 - 1984862880 z - 1902700800 z^2 + 17436131328 z^3 + 12208766976 z^4 + 1046478848 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(5411658792960 z^(17/4))

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]