Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9061)

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/07.22.03.9061.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(13/4)}, -z] == (2 Sqrt[z] (-27792237677329125 + 8538321867075000 z + 364301732995200 z^2 - 28158588057600 z^3 + 2059068211200 z^4 - 212548976640 z^5 + 39636172800 z^6 - 19730006016 z^7 + 109521666048 z^8 + 2147483648 z^9) Cos[2 Sqrt[z]] + 536870912 Sqrt[Pi] z^(35/4) (819 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (27792237677329125 - 45594638770180500 z + 1138442915610000 z^2 - 214709233939200 z^3 + 14820309504000 z^4 - 1248725237760 z^5 + 167462830080 z^6 - 47563407360 z^7 + 53955526656 z^8 + 1073741824 z^9) Sin[2 Sqrt[z]])/(548323430054400 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]