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

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`=11/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, 15/4}, -z] == (1/(57278464 z^(9/2))) (21 (Sqrt[Pi] z^(7/4) (7571025 - 6292800 z + 3356160 z^2 + 1884160 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (302400 + 460800 z - 394725 z^2 + 189360 z^3 + 116992 z^4 + 4096 z^5) Cos[2 Sqrt[z]] + (-604800 - 115200 z - 290385 z^2 + 114480 z^3 + 113920 z^4 + 4096 z^5) 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]