Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af39)

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=17/4, b_1`>=-11/2

For fixed z and a₁=17/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.af39.01

Input Form

HypergeometricPFQ[{17/4}, {-(9/2), 21/4}, -z] == (1/(3963617280 z^(17/4))) (17 (25949801752875 Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((25949801752875 - 27679788536400 z + 7029787564800 z^2 - 786549657600 z^3 + 49235558400 z^4 - 1766850560 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] - 20 Sqrt[z] (-1729986783525 + 790851101040 z - 127814319360 z^2 + 10487328768 z^3 - 507838464 z^4 + 11534336 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]