Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8749)

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`=-3/2

http://functions.wolfram.com/07.22.03.8749.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), 11/4}, -z] == (1/(1395193282560 z^(7/4))) (Sqrt[Pi] (-84666807225 - 243145702800 z + 1296777081600 z^2 - 1383228887040 z^3 + 2459073576960 z^4 + 605310418944 z^5 + 27128758272 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-28222269075 + 106252201440 z - 103536195840 z^2 + 147251478528 z^3 + 37520867328 z^4 + 1692401664 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (84666807225 + 152834441760 z - 138003022080 z^2 + 123930132480 z^3 + 36304257024 z^4 + 1679818752 z^5 + 16777216 z^6) 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]