Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa1z)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.aa1z.01

Input Form

HypergeometricPFQ[{-(7/4)}, {7/2, 21/4}, -z] == (1/(3221225472 z^(17/4))) (Sqrt[Pi] (-366522975 - 902210400 z + 4009824000 z^2 - 3421716480 z^3 + 4562288640 z^4 + 748683264 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((366522975 + 511252560 z - 343042560 z^2 + 245145600 z^3 + 45809664 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-122174325 + 321345360 z - 250790400 z^2 + 276799488 z^3 + 46596096 z^4 + 1048576 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]