Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8nd)

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`=3/2

http://functions.wolfram.com/07.22.03.a8nd.01

Input Form

HypergeometricPFQ[{-(13/4)}, {3/2, 23/4}, -z] == (19 (Sqrt[Pi] (4108830350625 + 2697078384000 z + 1525620096000 z^2 + 1394852659200 z^3 + 9299017728000 z^4 + 39675808972800 z^5 + 9068756336640 z^6 + 418759311360 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (1369610116875 + 272918646000 z + 198745747200 z^2 + 290594304000 z^3 + 2383517122560 z^4 + 562000035840 z^5 + 26122125312 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (-4108830350625 + 1685673990000 z + 238183545600 z^2 - 373621248000 z^3 + 2036122583040 z^4 + 543251496960 z^5 + 25920798720 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (692692325498880 z^(19/4))

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]