Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7469)

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=-15/4

http://functions.wolfram.com/07.22.03.7469.01

Input Form

HypergeometricPFQ[{5}, {-(15/4), 15/4}, -z] == (1/(1474560 z^(11/4))) (4 z^(3/4) (-4729725 + 2286900 z - 439200 z^2 - 181696 z^3 + 7168 z^4) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((14189175 - 31185000 z + 16178400 z^2 - 3951360 z^3 - 1290240 z^4 + 65536 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (14189175 - 12266100 z + 4868640 z^2 + 100800 z^3 - 317440 z^4 - 16384 z^5) Sin[2 Sqrt[z]]) - Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-14189175 + 12266100 z - 4868640 z^2 - 100800 z^3 + 317440 z^4 + 16384 z^5) Cos[2 Sqrt[z]] + (14189175 - 31185000 z + 16178400 z^2 - 3951360 z^3 - 1290240 z^4 + 65536 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]