Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9069)

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`=11/2

http://functions.wolfram.com/07.22.03.9069.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(5/4)}, -z] == (2 Sqrt[z] (-99613755115875 + 18149089959000 z + 1111523212800 z^2 - 1482030950400 z^3 + 623960064000 z^4 - 470184099840 z^5 + 3149754531840 z^6 + 381327507456 z^7 + 10292822016 z^8 + 67108864 z^9) Cos[2 Sqrt[z]] + 65536 Sqrt[Pi] z^(27/4) (196383915 + 23390640 z + 628992 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (99613755115875 - 150967430113500 z - 12330960642000 z^2 - 4075585113600 z^3 + 1886221209600 z^4 - 953249955840 z^5 + 1447050608640 z^6 + 186909327360 z^7 + 5121245184 z^8 + 33554432 z^9) Sin[2 Sqrt[z]])/(14059575129600 z^(9/2))

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]