Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9599)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9599.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(3/4)}, -z] == (1/(54820022400 z^(7/2))) (-2 Sqrt[z] (29462808375 + 3235131900 z + 5688144000 z^2 - 4572564480 z^3 + 8239841280 z^4 + 1619896320 z^5 + 61145088 z^6 + 524288 z^7) Cos[2 Sqrt[z]] - 2048 Sqrt[Pi] z^(21/4) (75004875 + 13091760 z + 481536 z^2 + 4096 z^3) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (29462808375 - 36048612600 z - 9101030400 z^2 + 10112256000 z^3 - 10024058880 z^4 + 74482974720 z^5 + 13315227648 z^6 + 492306432 z^7 + 4194304 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]