Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7397)

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, b₁>=-23/4

For fixed z and a₁=5, b₁=-21/4

http://functions.wolfram.com/07.22.03.7397.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), -(7/4)}, -z] == (1/13157235) (13157235 - 7160400 z + 6739200 z^2 - 23122800 z^3 - 4360704 z^4 - 1853952 z^5 + 8192 z^6 - 8 Sqrt[Pi] z^(11/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-27 (98325 - 115368 z - 47104 z^2 + 2048 z^3) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-2654775 - 424764 z - 238464 z^2 + 1024 z^3) Sin[2 Sqrt[z]]) + 8 Sqrt[Pi] z^(11/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-2654775 - 424764 z - 238464 z^2 + 1024 z^3) Cos[2 Sqrt[z]] + 27 (98325 - 115368 z - 47104 z^2 + 2048 z^3) 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]