Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8973)

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/07.22.03.8973.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(5/4)}, -z] == (1/(40556466720 z^(5/2))) (2 Sqrt[z] (-6512831325 - 4631346720 z + 3366800640 z^2 - 3074899968 z^3 + 22233415680 z^4 + 3648196608 z^5 + 127795200 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] + 1024 Sqrt[Pi] z^(19/4) (89343891 + 14342832 z + 499968 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (6512831325 - 4052428380 z + 8420630400 z^2 - 5779952640 z^3 + 9933815808 z^4 + 1777821696 z^5 + 63504384 z^6 + 524288 z^7) 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]