Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8br)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8br.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(11/4)}, -z] == (1/(625354329600 z^(9/2))) (-2 Sqrt[z] (55087698290625 - 18814846050000 z - 439977938400 z^2 + 17643225600 z^3 - 1107025920 z^4 + 123863040 z^5 - 31457280 z^6 + 33554432 z^7) Cos[2 Sqrt[z]] - 536870912 Sqrt[Pi] z^(33/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (55087698290625 - 92265110437500 z + 5059746291600 z^2 - 167610643200 z^3 + 8302694400 z^4 - 681246720 z^5 + 110100480 z^6 - 50331648 z^7 + 268435456 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]