Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aaj9)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aaj9.01

Input Form

HypergeometricPFQ[{-(5/4)}, {9/2, 19/4}, -z] == (1/(318767104 z^(15/4))) (7 (Sqrt[Pi] (-76039425 + 184338000 z - 120384000 z^2 + 58368000 z^3 + 31129600 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (11517525 - 7576320 z + 3310080 z^2 + 1933312 z^3 + 65536 z^4) Cos[2 Sqrt[z]] + (2311425 - 5924160 z + 2065920 z^2 + 1884160 z^3 + 65536 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]