Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.abzc)

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=3/4, b_1`>=-11/2

For fixed z and a₁=3/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.abzc.01

Input Form

HypergeometricPFQ[{3/4}, {-(9/2), 23/4}, -z] == -((1/(103079215104 z^(19/4))) (209 (69615 Sqrt[Pi] (3067304625 + 353707200 z + 23385600 z^2 + 1228800 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (71176803823125 - 24330191886000 z + 2049198278400 z^2 - 44635852800 z^3 + 134217728 z^4) Cos[2 Sqrt[z]] - 105 (2033622966375 - 1934689957200 z + 316270306560 z^2 - 13835530240 z^3 + 134217728 z^4) 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]