Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8937)

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`=5/2

http://functions.wolfram.com/07.22.03.8937.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 7/4}, -z] == (Sqrt[Pi] z^(3/4) (2846107289025 + 39032328535200 z + 28387148025600 z^2 + 4485870305280 z^3 + 217937018880 z^4 + 3567255552 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (38494310400 + 2193525981675 z + 1726681335120 z^2 + 277901729280 z^3 + 13579689984 z^4 + 222756864 z^5 + 1048576 z^6) Cos[2 Sqrt[z]] + (-76988620800 + 1465255475775 z + 1554829350480 z^2 + 268385564160 z^3 + 13415915520 z^4 + 221970432 z^5 + 1048576 z^6) Sin[2 Sqrt[z]]))/(26793433497600 z^(3/2))

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]