Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9wn)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a9wn.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(1/2), 21/4}, -z] == (1/(17179869184 z^(17/4))) (221 (Sqrt[Pi] (808782975 + 314344800 z + 93139200 z^2 + 36126720 z^3 + 61931520 z^4 - 44040192 z^5 - 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-808782975 + 548357040 z + 23063040 z^2 + 2580480 z^3 - 1769472 z^4 - 1048576 z^5) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-269594325 + 18461520 z - 3064320 z^2 - 3956736 z^3 + 2555904 z^4 + 1048576 z^5) 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]