Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7w1)

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`=11/2

http://functions.wolfram.com/07.22.03.a7w1.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(1/4)}, -z] == (1/(72100385280 z^(9/2))) (-2 Sqrt[z] (206239658625 - 28945917000 z + 6415718400 z^3 - 7411138560 z^4 + 57637601280 z^5 + 11699896320 z^6 + 467140608 z^7 + 4194304 z^8) Cos[2 Sqrt[z]] - 4096 Sqrt[Pi] z^(23/4) (58267755 + 11509680 z + 456960 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - (-206239658625 + 303932128500 z + 34735100400 z^2 + 11227507200 z^3 - 12831436800 z^4 + 25102909440 z^5 + 5681356800 z^6 + 231997440 z^7 + 2097152 z^8) 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]