Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9909)

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`=-3/2

http://functions.wolfram.com/07.22.03.9909.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(3/2), 19/4}, -z] == (11 (Sqrt[Pi] (-10075350059775 - 5582877955200 z - 2627236684800 z^2 - 2155681382400 z^3 + 4790403072000 z^4 - 2452686372864 z^5 + 2180165664768 z^6 + 255550554112 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-3358450019925 - 325667880720 z - 273149210880 z^2 + 351799160832 z^3 - 172971982848 z^4 + 133375721472 z^5 + 15921577984 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (10075350059775 - 5164162108560 z - 598426133760 z^2 + 560306073600 z^3 - 230934380544 z^4 + 122277593088 z^5 + 15720251392 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (69269232549888 z^(15/4))

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]