Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8m1)

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`=1/2

http://functions.wolfram.com/07.22.03.a8m1.01

Input Form

HypergeometricPFQ[{-(13/4)}, {1/2, 23/4}, -z] == (19 (Sqrt[Pi] (-4656674397375 - 2337467932800 z - 915372057600 z^2 - 464950886400 z^3 - 619934515200 z^4 + 7935161794560 z^5 + 4232086290432 z^6 + 307090161664 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-1552224799125 - 69567498000 z - 63619395840 z^2 - 63653990400 z^3 + 453543788544 z^4 + 261016780800 z^5 + 19142803456 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (4656674397375 - 2629651424400 z - 316436440320 z^2 - 19372953600 z^3 + 309967257600 z^4 + 247502733312 z^5 + 18941476864 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/(92358976733184 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]