Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8s9)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8s9.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 7/4}, -z] == (1/(686670336 z^(9/2))) (2 Sqrt[z] (42567525 + 5896800 z + 9266400 z^2 + 31449600 z^3 + 173773932 z^4 + 37301952 z^5 + 1647616 z^6 + 16384 z^7) Cos[2 Sqrt[z]] + Sqrt[Pi] z^(15/4) (213974865 + 720757440 z + 150418944 z^2 + 6602752 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (-42567525 + 50859900 z + 13731120 z^2 - 11232000 z^3 + 75243870 z^4 + 18058848 z^5 + 817664 z^6 + 8192 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]