Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ut)

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`=9/2

http://functions.wolfram.com/07.22.03.a7ut.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 3/4}, -z] == (1/(4635024768 z^(7/2))) (2 Sqrt[z] (-103378275 - 47616660 z - 85924800 z^2 + 1637369856 z^3 + 1200338520 z^4 + 141266304 z^5 + 4311040 z^6 + 32768 z^7) Cos[2 Sqrt[z]] + 2 Sqrt[Pi] z^(15/4) (3637572705 + 2450575296 z + 284124672 z^2 + 8634368 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (103378275 - 90221040 z - 14320800 z^2 + 534643200 z^3 + 553479804 z^4 + 69067968 z^5 + 2143232 z^6 + 16384 z^7) 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]