Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8pt)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a8pt.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, 15/4}, -z] == (1/(329923952640 z^(11/4))) (Sqrt[Pi] (18602008425 - 85037752800 z + 161976672000 z^2 + 314136576000 z^3 + 50261852160 z^4 + 1881145344 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-4150741725 + 7464759120 z + 19090091520 z^2 + 3119751168 z^3 + 117374976 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (2100813975 - 14405040 z + 17087915520 z^2 + 3035013120 z^3 + 116588544 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]