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

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`=-11/2

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

Input Form

HypergeometricPFQ[{3/4}, {-(11/2), 19/4}, -z] == (1/(805306368 z^(15/4))) (-1740375 Sqrt[Pi] (8179479 + 964656 z + 66816 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (4745120254875 - 1609576768800 z + 133512288000 z^2 - 2863661056 z^3 + 8388608 z^4) Cos[2 Sqrt[z]] + (-14235360764625 + 13505521629600 z - 2181849196800 z^2 + 93585408000 z^3 - 889192448 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]