Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9997)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.9997.01

Input Form

HypergeometricPFQ[{-(17/4)}, {1/2, 11/4}, -z] == (1/(62285414400 z^(7/4))) (Sqrt[Pi] (-516891375 - 3308104800 z + 132324192000 z^2 + 188194406400 z^3 + 35846553600 z^4 + 1604321280 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-172297125 + 6761739600 z + 11380538880 z^2 + 2222039040 z^3 + 100073472 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (516891375 + 2756754000 z + 9997309440 z^2 + 2150277120 z^3 + 99287040 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]