Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8989)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8989.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 11/4}, -z] == (Sqrt[Pi] z^(3/4) (-264687977879325 + 1411669215356400 z + 6160011121555200 z^2 + 2190226176552960 z^3 + 204933443420160 z^4 + 6579802865664 z^5 + 76453773312 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-6467044147200 + 49734282513825 z + 363681065492640 z^2 + 134644636143360 z^3 + 12733150445568 z^4 + 410348617728 z^5 + 4775215104 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] + (12934088294400 - 28484690127075 z + 292672903592160 z^2 + 126250536625920 z^3 + 12439890247680 z^4 + 406819897344 z^5 + 4762632192 z^6 + 16777216 z^7) Sin[2 Sqrt[z]]))/ (5315817205923840 z^(5/2))

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]